Why no flat topped windows?

[Richard Owlett]

I'm looking at comparing FFT's of a batch of signals.
Right now I'm choosing how to window the input data.
I noticed that none of the _common_ windows have flat top except for the
"rectangular window".

Is there a reason other than the simplicity of calculating the window
function? I was thinking about piecewise continuous with continuous
first derivative.

[Rune Allnor]

On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
> I'm looking at comparing FFT's of a batch of signals.
> Right now I'm choosing how to window the input data.
> I noticed that none of the _common_ windows have flat top except for the
> "rectangular window".
>
> Is there a reason other than the simplicity of calculating the window
> function? I was thinking about piecewise continuous with continuous
> first derivative.

There is the Tukey window, which I think has a "flat" top.

FIR filter design by window functions is all but obsolete
after methods like Parks-McClellan were developed. So the
detailed analysis of window functions is not all that
interesting these days...

Rune

[Richard Owlett]

Rune Allnor wrote:
> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
>
>>I'm looking at comparing FFT's of a batch of signals.
>>Right now I'm choosing how to window the input data.
>>I noticed that none of the _common_ windows have flat top except for the
>>"rectangular window".
>>
>>Is there a reason other than the simplicity of calculating the window
>>function? I was thinking about piecewise continuous with continuous
>>first derivative.
>
>
> There is the Tukey window, which I think has a "flat" top.
>
> FIR filter design by window functions is all but obsolete
> after methods like Parks-McClellan were developed. So the
> detailed analysis of window functions is not all that
> interesting these days...
>
> Rune
>

OK? or perhaps ???? ;)
I understood windowing data prior to doing an fft was required to reduce
spectral leakage.

What did I say that brought filters to mind?

[robert bristow-johnson]

On Oct 28, 9:37 am, Richard Owlett <[email protected]> wrote:
> I'm looking at comparing FFT's of a batch of signals.
> Right now I'm choosing how to window the input data.
> I noticed that none of the _common_ windows have flat top except for the
> "rectangular window".
>
> Is there a reason other than the simplicity of calculating the window
> function? I was thinking about piecewise continuous with continuous
> first derivative.

a window i suggested (in an AES article in 1995) for use in audio
splicing (i like to think of a window as the concatination of two
splicing functions, a fade up followed by a fade down) is:

w(t) = (1/2)*( 1 + (9/8)*cos(pi*t) - (1/8)*cos(3*pi*t) )

for -1 <= t <= +1 ( w(t) = 0 for |t| > 1 )


it's a sorta extension to the Hann window,:

w(t) = (1/2)*( 1 + cos(pi*t) )

for -1 <= t <= +1 ( w(t) = 0 for |t| > 1 )

the Hann window is continuous everywhere in the 0th and 1st derivative
with a discontinuity in the 2nd derivative at the two points where the
operative part of the window is appended to silence (at t=-1 and t=
+1).

this "flattened Hann" (what i call it until somebody points to a prior
reference) is continuous everywhere through the 2nd derivative and has
discontinuity at the 3rd and higher derivatives at +1 and -1.


r b-j

[Jerry Avins]

Richard Owlett wrote:
> I'm looking at comparing FFT's of a batch of signals.
> Right now I'm choosing how to window the input data.
> I noticed that none of the _common_ windows have flat top except for the
> "rectangular window".
>
> Is there a reason other than the simplicity of calculating the window
> function? I was thinking about piecewise continuous with continuous
> first derivative.

A continuous and *finite* first derivative? Think what that implies.
Points of sharp curvature -- i.e., large second derivative -- aren't
helpful.

A window is almost always computed off line. Simplicity isn't a major
consideration.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Ron N.]

On Oct 28, 6:37 am, Richard Owlett <[email protected]> wrote:
> I'm looking at comparing FFT's of a batch of signals.
> Right now I'm choosing how to window the input data.
> I noticed that none of the _common_ windows have flat top except for the
> "rectangular window".

I've also seen trapezoidal windows mentioned. The flatter
the top in proportion to the total, the steeper the sides
need to be for a side of similar shape. Steeper sides
usually correspond to more high frequency content in the
transform, which is often what one doesn't want from a window
function.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

[Erik de Castro Lopo]

Richard Owlett wrote:

> I'm looking at comparing FFT's of a batch of signals.
> Right now I'm choosing how to window the input data.
> I noticed that none of the _common_ windows have flat top except for the
> "rectangular window".
>
> Is there a reason other than the simplicity of calculating the window
> function?

I played around with this idea years ago and my experimentation showed
that all the the flat top windows I could find or think of suffered
from worse spectral leakage effects that all of the traditional windows.

Erik
--
-----------------------------------------------------------------
Erik de Castro Lopo
-----------------------------------------------------------------
Complex problems have simple easy to understand wrong answers.

[Jerry Avins]

Erik de Castro Lopo wrote:
> Richard Owlett wrote:
>
>> I'm looking at comparing FFT's of a batch of signals.
>> Right now I'm choosing how to window the input data.
>> I noticed that none of the _common_ windows have flat top except for the
>> "rectangular window".
>>
>> Is there a reason other than the simplicity of calculating the window
>> function?
>
> I played around with this idea years ago and my experimentation showed
> that all the the flat top windows I could find or think of suffered
> from worse spectral leakage effects that all of the traditional windows.

That shouldn't be too surprising. Windows suppress ringing in filters,
while they reduce spillover in FTs. The two actions are related, so one
can reason about both from either vantage point. In filters, steeper
sides make for more ringing. In windows, steeper sides make for less
suppression of ringing. The more the top stays flat, the steeper the
sides need to be.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[dbd]

On Oct 28, 12:34 pm, robert bristow-johnson
<[email protected]> wrote:
> On Oct 28, 9:37 am, Richard Owlett <[email protected]> wrote:
>
> > I'm looking at comparing FFT's of a batch of signals.
> > Right now I'm choosing how to window the input data.
> > I noticed that none of the _common_ windows have flat top except for the
> > "rectangular window".
>
> > Is there a reason other than the simplicity of calculating the window
> > function? I was thinking about piecewise continuous with continuous
> > first derivative.
>
> a window i suggested (in an AES article in 1995) for use in audio
> splicing (i like to think of a window as the concatination of two
> splicing functions, a fade up followed by a fade down) is:
>
> w(t) = (1/2)*( 1 + (9/8)*cos(pi*t) - (1/8)*cos(3*pi*t) )
>
> for -1 <= t <= +1 ( w(t) = 0 for |t| > 1 )
>
> it's a sorta extension to the Hann window,:
>
> w(t) = (1/2)*( 1 + cos(pi*t) )
>
> for -1 <= t <= +1 ( w(t) = 0 for |t| > 1 )
>
> the Hann window is continuous everywhere in the 0th and 1st derivative
> with a discontinuity in the 2nd derivative at the two points where the
> operative part of the window is appended to silence (at t=-1 and t=
> +1).
>
> this "flattened Hann" (what i call it until somebody points to a prior
> reference) is continuous everywhere through the 2nd derivative and has
> discontinuity at the 3rd and higher derivatives at +1 and -1.
>
> r b-j

For a quick comparison of Hann and flattened Hann:

Hann
Transform Size: 256 Bins Coherent Gain: 0.5
Eff. Noise BW: 1.5 Bins Scalloping/Wcae: -1.4236 dB
-3 dB BW: 1.45 Bins Mainlobe Width: 4 Bins
-6 dB BW: 2.02 Bins Max. Sidelobe: -31.47 dB
-60 dB BW: 13.3 Bins Max. SSL BW: 3.75 Bins
SL Falloff: -18.06 dB/Octave Bin 1 SL Intcpt:-9.92 dB

flattenedHann
Transform Size: 256 Bins Coherent Gain: 0.5
Eff. Noise BW: 1.6406 Bins Scalloping/Wcae: -1.1789 dB
-3 dB BW: 1.58 Bins Mainlobe Width: 4 Bins
-6 dB BW: 2.19 Bins Max. Sidelobe: -21.81 dB
-60 dB BW: 9.66 Bins Max. SSL BW: 3.56 Bins
SL Falloff: -30.1 dB/Octave Bin 1 SL Intcpt: 9.43 dB

The flattened version rolls off at -30 dB/oct versus -18 dB/oct. for
Hann, but in the region from 2 to 4 bin widths from the bin center,
response of the flattened version can be almost 20 dB higher than the
Hann response; the typical/near far window tradeoff.

Dale B. Dalrymple
http://dbdimages.com
http://stores.lulu.com/dbd

[Fred Marshall]

"Ron N." <[email protected]> wrote in message
news:[email protected] oups.com...
> On Oct 28, 6:37 am, Richard Owlett <[email protected]> wrote:
>> I'm looking at comparing FFT's of a batch of signals.
>> Right now I'm choosing how to window the input data.
>> I noticed that none of the _common_ windows have flat top except for the
>> "rectangular window".
>
> I've also seen trapezoidal windows mentioned. The flatter
> the top in proportion to the total, the steeper the sides
> need to be for a side of similar shape. Steeper sides
> usually correspond to more high frequency content in the
> transform, which is often what one doesn't want from a window
> function.
>

heh ..... that would be the convolution of two gate functions. When they
are the same length then you get a triangular result. When one is narrower
than the other, you get a flat top. When one is much narrower than the
other you get quite a wide flat top.

Now let's look in frequency:
Multiply the ffts of those gate functions - which are sinc functions.

- If the gates are the same length and you have a triangular function then
the fft is a sin^2(x)/x^2. The decay is then proportional to 1/f^3 as I
recall ... instead of 1/f for the sinc. The decay is related to the order
of the zero at the edge in time.

- If the gates are very different in length then you have a long flat top
and linearly tapered ends - half a triangle. In this case the fft of the
narrow one is wide and the fft of the wide one is narrow. Those are
multiplied together so you will have the narrow sinx/x shape but while with
more rapidly decaying tails than the sinc and about the same first sidelobes
as the narrow sinc.

Another variation is to use a cosine taper at the edges. The widest version
is a raised cosine with DFT of [1/4 1/2 1/4]. Narrowing the cosine taper at
the ends and adding a flat top gets the flat-topped versions. Maybe not as
good in frequency as the trapezoidal one.

You might ask a couple of questions:
1) Why window at all?
2) Why care about a flat top if you do?

Fred

[dbd]

On Oct 28, 4:59 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:

.. You might ask a couple of questions:
.. 1) Why window at all?
.. 2) Why care about a flat top if you do?
..
.. Fred

1) You can't complete a calculation on data without windowing.
2) Errant curiosity.

Dale B. Dalrymple
http://dbdimages.com
http://stores.lulu.com/dbd

[Fred Marshall]

"dbd" <[email protected]> wrote in message
news:[email protected] ups.com...
> On Oct 28, 4:59 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
> wrote:
>
> . You might ask a couple of questions:
> . 1) Why window at all?
> . 2) Why care about a flat top if you do?
> .
> . Fred
>
> 1) You can't complete a calculation on data without windowing.
> 2) Errant curiosity.
>
> Dale B. Dalrymple
> http://dbdimages.com
> http://stores.lulu.com/dbd


Define "complete" would you?

Do you mean "inherent curiosity"?

[Ron N.]

On Oct 28, 10:24 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
> "dbd" <[email protected]> wrote in message
>
> news:[email protected] ups.com...
>
> > On Oct 28, 4:59 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
> > wrote:
>
> > . You might ask a couple of questions:
> > . 1) Why window at all?
> > . 2) Why care about a flat top if you do?
> > .
> > . Fred
>
> > 1) You can't complete a calculation on data without windowing.
> > 2) Errant curiosity.
>
> > Dale B. Dalrymple
> >http://dbdimages.com
> >http://stores.lulu.com/dbd
>
> Define "complete" would you?

A calculation on data that finishes in finite bounded
time?

Unwindowed data could be considered infinite in extent
in some contexts. Thus any finite sampled data set would
have at least a rectangular window of length no longer
than the existence or extent of the sampling mechanism.




IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

[Richard Owlett]

Fred Marshall wrote:
> "dbd" <[email protected]> wrote in message
> news:[email protected] ups.com...
>
>>On Oct 28, 4:59 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
>>wrote:
>>
>>. You might ask a couple of questions:
>>. 1) Why window at all?
>>. 2) Why care about a flat top if you do?
>>.
>>. Fred
>>
>>1) You can't complete a calculation on data without windowing.
>>2) Errant curiosity.
>>
>>Dale B. Dalrymple
>>http://dbdimages.com
>>http://stores.lulu.com/dbd
>
>
>
> Define "complete" would you?
>
> Do you mean "inherent curiosity"?
>
>

I'd have to say my inherent curiosity was somewhat errant.

In other words, I didn't ask the wrong question - just not quite the
right one. Now to determine just what is the right one ;/

[Chris Bore]

On Oct 28, 2:37 pm, Richard Owlett <[email protected]> wrote:
> I'm looking at comparing FFT's of a batch of signals.
> Right now I'm choosing how to window the input data.
> I noticed that none of the _common_ windows have flat top except for the
> "rectangular window".
>
> Is there a reason other than the simplicity of calculating the window
> function? I was thinking about piecewise continuous with continuous
> first derivative.

The shape of a Window function in time domain determines its shape in
the spectrum.

The purpose of a time-domain Window is to impose a well-defined shape
in the frequency domain. So the time domain shape is derived from the
desired frequency shape. For instance the 'Harris Flat Top' window has
a flat top - in the frequency domain - rather than in its time domain
shape.

Normally you desire smooth transitions and a mathematically defined
formula so the window's spectral shape can be calculate analytically.
Also the Widnow should have a spectral shape that is band limited,
which tends to mean that flat tops are hard to do.

I discuss FFT window functions on my web site:

http://www.bores.com/courses/advanced/windows/index.htm

if you're interested.

Chris
=========================
Chris Bore
BORES Signal Processing
www.bores.com

[Chris Bore]

>FIR filter design by window functions is all but obsolete
>after methods like Parks-McClellan were developed. So the
>detailed analysis of window functions is not all that
>interesting these days...

Umm. Parks-McLellan gives the 'best' filter if you mean by 'best',
'least mean squares approximation'.
Other iterative filter design methods each aim for their own type of
'best' approximation, but I do not think they necessarily make FIR
window filter design obsolete or uninteresting. Sometimes we want some
other approximation. Or sometimes we want a filter whose shape can be
processed analytically rather than numerically.

And, the choice of appropriate window to apply before an FFT is not
quite the same problem as using a window to design an FIR filter.

Chris
==========================
Chris Bore
BORES Signal Processing
www.bores.com




On Oct 28, 4:15 pm, Rune Allnor <[email protected]> wrote:
> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
>
> > I'm looking at comparing FFT's of a batch of signals.
> > Right now I'm choosing how to window the input data.
> > I noticed that none of the _common_ windows have flat top except for the
> > "rectangular window".
>
> > Is there a reason other than the simplicity of calculating the window
> > function? I was thinking about piecewise continuous with continuous
> > first derivative.
>
> There is the Tukey window, which I think has a "flat" top.
>
> FIR filter design by window functions is all but obsolete
> after methods like Parks-McClellan were developed. So the
> detailed analysis of window functions is not all that
> interesting these days...
>
> Rune

[Richard Owlett]

Chris Bore wrote:
> On Oct 28, 2:37 pm, Richard Owlett <[email protected]> wrote:
>
>>I'm looking at comparing FFT's of a batch of signals.
>>Right now I'm choosing how to window the input data.
>>I noticed that none of the _common_ windows have flat top except for the
>>"rectangular window".
>>
>>Is there a reason other than the simplicity of calculating the window
>>function? I was thinking about piecewise continuous with continuous
>>first derivative.
>
>
> The shape of a Window function in time domain determines its shape in
> the spectrum.
>
> The purpose of a time-domain Window is to impose a well-defined shape
> in the frequency domain. So the time domain shape is derived from the
> desired frequency shape. For instance the 'Harris Flat Top' window has
> a flat top - in the frequency domain - rather than in its time domain
> shape.
>
> Normally you desire smooth transitions and a mathematically defined
> formula so the window's spectral shape can be calculate analytically.
> Also the Widnow should have a spectral shape that is band limited,
> which tends to mean that flat tops are hard to do.
>
> I discuss FFT window functions on my web site:
>
> http://www.bores.com/courses/advanced/windows/index.htm
>
> if you're interested.
>

I'm *INTERESTED* ;)
Actually I've been there in past but I suspect I'm about have an "AHAAA
of course" moment. Some concepts are about to gel.

[[email protected]]

On Oct 29, 7:46 am, Chris Bore <[email protected]> wrote:
> >FIR filter design by window functions is all but obsolete
> >after methods like Parks-McClellan were developed. So the
> >detailed analysis of window functions is not all that
> >interesting these days...
>
> Umm. Parks-McLellan gives the 'best' filter if you mean by 'best',
> 'least mean squares approximation'.
> Other iterative filter design methods each aim for their own type of
> 'best' approximation, but I do not think they necessarily make FIR
> window filter design obsolete or uninteresting. Sometimes we want some
> other approximation. Or sometimes we want a filter whose shape can be
> processed analytically rather than numerically.
>
> And, the choice of appropriate window to apply before an FFT is not
> quite the same problem as using a window to design an FIR filter.
>
> Chris
> ==========================
> Chris Bore
> BORES Signal Processingwww.bores.com

Chris, correct me if I'm wrong but the PM algorithm is a MiniMax
algorithm not least squares - there is no constraint on the mean error
energy. Least squares is different algorithm.

Cheers,
David

[Jerry Avins]

Fred Marshall wrote:
> "dbd" <[email protected]> wrote in message
> news:[email protected] ups.com...
>> On Oct 28, 4:59 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
>> wrote:
>>
>> . You might ask a couple of questions:
>> . 1) Why window at all?
>> . 2) Why care about a flat top if you do?
>> .
>> . Fred
>>
>> 1) You can't complete a calculation on data without windowing.
>> 2) Errant curiosity.
>>
>> Dale B. Dalrymple
>> http://dbdimages.com
>> http://stores.lulu.com/dbd
>
>
> Define "complete" would you?
>
> Do you mean "inherent curiosity"?

"Errant" means "wandering". Some people use it to mean "misdirected".

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[dbd]

On Oct 29, 6:12 am, Jerry Avins <[email protected]> wrote:
> Fred Marshall wrote:
> > "dbd" <[email protected]> wrote in message
> >news:[email protected] ups.com...
> >> On Oct 28, 4:59 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
> >> wrote:
>
> >> . You might ask a couple of questions:
> >> . 1) Why window at all?
> >> . 2) Why care about a flat top if you do?
> >> .
> >> . Fred
>
> >> 1) You can't complete a calculation on data without windowing.
> >> 2) Errant curiosity.
>
> >> Dale B. Dalrymple
> >>http://dbdimages.com
> >>http://stores.lulu.com/dbd
>
> > Define "complete" would you?
>
> > Do you mean "inherent curiosity"?
>
> "Errant" means "wandering". Some people use it to mean "misdirected".
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

For "complete": "make the final included operation"

For "errant" Dictionary.com also includes "roving adventurously".

Dale B. Dalrymple
http://dbdimages.com
http://stores.lulu.com/dbd

[Peter K.]

[email protected] writes:

> On Oct 29, 7:46 am, Chris Bore <[email protected]> wrote:
> > >FIR filter design by window functions is all but obsolete
> > >after methods like Parks-McClellan were developed. So the
> > >detailed analysis of window functions is not all that
> > >interesting these days...
> >
> > Umm. Parks-McLellan gives the 'best' filter if you mean by 'best',
> > 'least mean squares approximation'.
> > Other iterative filter design methods each aim for their own type of
> > 'best' approximation, but I do not think they necessarily make FIR
> > window filter design obsolete or uninteresting. Sometimes we want some
> > other approximation. Or sometimes we want a filter whose shape can be
> > processed analytically rather than numerically.
> >
> > And, the choice of appropriate window to apply before an FFT is not
> > quite the same problem as using a window to design an FIR filter.
> >
> > Chris
> > ==========================
> > Chris Bore
> > BORES Signal Processingwww.bores.com
>
> Chris, correct me if I'm wrong but the PM algorithm is a MiniMax
> algorithm not least squares - there is no constraint on the mean error
> energy. Least squares is different algorithm.

That's true... the minimum mean square error filter would just be an
FIR filter designed using the window technique, with a rectangular
window --- which is rarely what one actually wants in a filer.

I agree with Chris that writing off windowed design is wrong, though.
There are some interesting things you can do with windowing.

Ciao,

Peter K.


--
"And he sees the vision splendid
of the sunlit plains extended
And at night the wondrous glory of the everlasting stars."

[Mark Borgerding]

Rune Allnor wrote:
> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
>> I'm looking at comparing FFT's of a batch of signals.
>> Right now I'm choosing how to window the input data.
>> I noticed that none of the _common_ windows have flat top except for the
>> "rectangular window".
>>
>> Is there a reason other than the simplicity of calculating the window
>> function? I was thinking about piecewise continuous with continuous
>> first derivative.
>
> There is the Tukey window, which I think has a "flat" top.
>
> FIR filter design by window functions is all but obsolete
> after methods like Parks-McClellan were developed. So the
> detailed analysis of window functions is not all that
> interesting these days...
>
> Rune
>

AFAIK, Parks-McClellan, AKA Remez Exchange filters must be verified
before use since it may not not converge to a solution.

Windowed design is still needed where predictability and stability is
more important than squeezing the utmost out of every coefficient.

Also, window design works just fine with really long filters.

-- Mark

[Chris Bore]

I think in fact Parks McLellan design(s) typically use either MiniMax
or LMS - depending whether you wish to specify minimum stop-band
attenuation and maximum pass-band error, or constraints on signal
energy.

Although, as Parks explains better than I can (in his book, Digital
Filter Design written with Burrus), in truth the desired approximation
is a matter of choice and there are other approximations than either
Chebyshev or least squares. Actually, that book by Parks is I think
one of the better texts on filter design, although I do not think it
is for beginners. He discusses several approximations, and also
discusses window design in the same context as iterative apprximation
methods.

Chris
=================
Chris Bore
BORES Signal Processing
www.bores.com


On Oct 29, 1:07 pm, [email protected] wrote:
> On Oct 29, 7:46 am, Chris Bore <[email protected]> wrote:
>
>
>
>
>
> > >FIR filter design by window functions is all but obsolete
> > >after methods like Parks-McClellan were developed. So the
> > >detailed analysis of window functions is not all that
> > >interesting these days...
>
> > Umm. Parks-McLellan gives the 'best' filter if you mean by 'best',
> > 'least mean squares approximation'.
> > Other iterative filter design methods each aim for their own type of
> > 'best' approximation, but I do not think they necessarily make FIR
> > window filter design obsolete or uninteresting. Sometimes we want some
> > other approximation. Or sometimes we want a filter whose shape can be
> > processed analytically rather than numerically.
>
> > And, the choice of appropriate window to apply before an FFT is not
> > quite the same problem as using a window to design an FIR filter.
>
> > Chris
> > ==========================
> > Chris Bore
> > BORES Signal Processingwww.bores.com
>
> Chris, correct me if I'm wrong but the PM algorithm is a MiniMax
> algorithm not least squares - there is no constraint on the mean error
> energy. Least squares is different algorithm.
>
> Cheers,
> David- Hide quoted text -
>
> - Show quoted text -

[Fred Marshall]

"Mark Borgerding" <[email protected]> wrote in message
news:[email protected]...
> Rune Allnor wrote:
>> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
>>> I'm looking at comparing FFT's of a batch of signals.
>>> Right now I'm choosing how to window the input data.
>>> I noticed that none of the _common_ windows have flat top except for the
>>> "rectangular window".
>>>
>>> Is there a reason other than the simplicity of calculating the window
>>> function? I was thinking about piecewise continuous with continuous
>>> first derivative.
>>
>> There is the Tukey window, which I think has a "flat" top.
>>
>> FIR filter design by window functions is all but obsolete
>> after methods like Parks-McClellan were developed. So the
>> detailed analysis of window functions is not all that
>> interesting these days...
>>
>> Rune
>>
>
> AFAIK, Parks-McClellan, AKA Remez Exchange filters must be verified before
> use since it may not not converge to a solution.

Maybe but you verify by running it - not before. Not a huge cost.

>
> Windowed design is still needed where predictability and stability is more
> important than squeezing the utmost out of every coefficient.

What predicability and stability do you refer to here? It appears you mean
the predictability of being able to achieve a design. P-M is so easy to try
that it's always a first step for me. If it fails, then I've only wasted a
couple of minutes.

>
> Also, window design works just fine with really long filters.
>

Good point!

[robert bristow-johnson]

On Oct 30, 10:41 pm, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
> "Mark Borgerding" <[email protected]> wrote in message
>
> news:[email protected]...
>
>
>
> > Rune Allnor wrote:
> >> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
> >>> I'm looking at comparing FFT's of a batch of signals.
> >>> Right now I'm choosing how to window the input data.
> >>> I noticed that none of the _common_ windows have flat top except for the
> >>> "rectangular window".
>
> >>> Is there a reason other than the simplicity of calculating the window
> >>> function? I was thinking about piecewise continuous with continuous
> >>> first derivative.
>
> >> There is the Tukey window, which I think has a "flat" top.
>
> >> FIR filter design by window functions is all but obsolete
> >> after methods like Parks-McClellan were developed. So the
> >> detailed analysis of window functions is not all that
> >> interesting these days...
>
> >> Rune
>
> > AFAIK, Parks-McClellan, AKA Remez Exchange filters must be verified before
> > use since it may not not converge to a solution.
>
> Maybe but you verify by running it - not before. Not a huge cost.
>
>
>
> > Windowed design is still needed where predictability and stability is more
> > important than squeezing the utmost out of every coefficient.
>
> What predicability and stability do you refer to here? It appears you mean
> the predictability of being able to achieve a design. P-M is so easy to try
> that it's always a first step for me. If it fails, then I've only wasted a
> couple of minutes.

for audio apps, remember that the equi-ripple in the P-McC passband is
not merely constant amplitude of the ripple but looks almost like
constant frequency. this is modulation in the frequency domain that
causes a pre-echo as well as a post-echo in the time-domain impulse
response. for audio, the pre-echo is very bad (perceptually
salient). as a little throwback check out problem 4 at:
http://www.circuitcellar.com/library/eq/154/index.htm and the answer
at: http://www.circuitcellar.com/library/eq/154/4.htm .

r b-j

[Fred Marshall]

"robert bristow-johnson" <[email protected]> wrote in message
news:[email protected] ups.com...

>
> for audio apps, remember that the equi-ripple in the P-McC passband is
> not merely constant amplitude of the ripple but looks almost like
> constant frequency. this is modulation in the frequency domain that
> causes a pre-echo as well as a post-echo in the time-domain impulse
> response. for audio, the pre-echo is very bad (perceptually
> salient). as a little throwback check out problem 4 at:
> http://www.circuitcellar.com/library/eq/154/index.htm and the answer
> at: http://www.circuitcellar.com/library/eq/154/4.htm .
>
> r b-j


hmmmmm.... interesting.

You remind me of a design I once did of an "all-pass" echo elongator for
sonar target simulation. The idea was that there would be a FIR filter that
would "elongate" any sonar ping so the resulting "echo" would have the
temporal elongation associated with a large reflective body.

Of course, the trivial all-pass is a unit sample - so no elongation. The
challenge was to design a FIR filter of some length that was close to
all-pass. And, I chose to use minimax.

The resulting "filters" have a sinusoidal (or nearly so) amplitude response.
So, they must have the same pre-echo and post-echo character .... ?

WAitaminnit ... this isn't frequency modulation in the normal sense because
it remains a linear system. So the thingies that you're mentioning must
occur during the transient response. ???

Fred

[robert bristow-johnson]

On Oct 31, 12:34 am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
> "robert bristow-johnson" <[email protected]> wrote in message
>
> news:[email protected] ups.com...
>
>
>
> > for audio apps, remember that the equi-ripple in the P-McC passband is
> > not merely constant amplitude of the ripple but looks almost like
> > constant frequency. this is modulation in the frequency domain that
> > causes a pre-echo as well as a post-echo in the time-domain impulse
> > response. for audio, the pre-echo is very bad (perceptually
> > salient). as a little throwback check out problem 4 at:
> >http://www.circuitcellar.com/library/eq/154/index.htmand the answer
> > at:http://www.circuitcellar.com/library/eq/154/4.htm.
>
> > r b-j
>
....
>
> The resulting "filters" have a sinusoidal (or nearly so) amplitude response.
> So, they must have the same pre-echo and post-echo character .... ?
>
> WAitaminnit ... this isn't frequency modulation in the normal sense because
> it remains a linear system. So the thingies that you're mentioning must
> occur during the transient response. ???

all's i was saying (when this first came up a few years ago here and
then somehow got into that Circuit Cellar thing) is that if you can
accurately represent your LPF response as a product of a more ideal
LPF (we'll call G(f)) times a cosine on a platform:


H(f) = G(f) * (1 + r*cos(2*pi*f*tau)) = G(f) +
r*G(f)*cos(2*pi*f*tau))

then the impulse response will look like:

h(t) = (r/2)*g(t+tau) + g(t) + (r/2)*g(t-tau)

so you have the impulse response of the "more ideal" LPF with scaled
(by r/2) copies of it both preceding and following the ideal LPF.
let's say that r << 1, the copy of the impulse response that comes
after g(t) gets wiped out, perceptually, by the main impulse
response. that's like not noticing a twitch in your face right after
i just slapped it hard (that twitch might be masked by the latent
tingling of the slap). but what if your face twitched just before the
slap?

sorry, i'm into violent allusions at the moment. a product of 7 years
exposure to "Fearless Leader" (a.k.a. the Abmonination in the White
House).

r b-j

[Mark Borgerding]

Fred Marshall wrote:
> "Mark Borgerding" <[email protected]> wrote in message
> news:[email protected]...
>> Rune Allnor wrote:
>>> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
>>>> I'm looking at comparing FFT's of a batch of signals.
>>>> Right now I'm choosing how to window the input data.
>>>> I noticed that none of the _common_ windows have flat top except for the
>>>> "rectangular window".
>>>>
>>>> Is there a reason other than the simplicity of calculating the window
>>>> function? I was thinking about piecewise continuous with continuous
>>>> first derivative.
>>> There is the Tukey window, which I think has a "flat" top.
>>>
>>> FIR filter design by window functions is all but obsolete
>>> after methods like Parks-McClellan were developed. So the
>>> detailed analysis of window functions is not all that
>>> interesting these days...
>>>
>>> Rune
>>>
>> AFAIK, Parks-McClellan, AKA Remez Exchange filters must be verified before
>> use since it may not not converge to a solution.
>
> Maybe but you verify by running it - not before. Not a huge cost.

If you are writing a program that designs a filter and then runs it,
what should the program do if it fails verification?

>
>> Windowed design is still needed where predictability and stability is more
>> important than squeezing the utmost out of every coefficient.
>
> What predicability and stability do you refer to here? It appears you mean
> the predictability of being able to achieve a design. P-M is so easy to try
> that it's always a first step for me. If it fails, then I've only wasted a
> couple of minutes.

Fine, but for a system that autonomously generates and executes a
filter, I'll stick with window design.


--
Mark Borgerding
3dB Labs, Inc
Innovate. Develop. Deliver.

[robert bristow-johnson]

On Oct 31, 4:04 pm, Mark Borgerding <[email protected]> wrote:
> Fred Marshall wrote:
> > "Mark Borgerding" <[email protected]> wrote in message
> >news:[email protected]...
> >> Rune Allnor wrote:
> >>> On 28 Okt, 14:37, Richard Owlett <[email protected]> wrote:
> >>>> I'm looking at comparing FFT's of a batch of signals.
> >>>> Right now I'm choosing how to window the input data.
> >>>> I noticed that none of the _common_ windows have flat top except for the
> >>>> "rectangular window".
>
> >>>> Is there a reason other than the simplicity of calculating the window
> >>>> function? I was thinking about piecewise continuous with continuous
> >>>> first derivative.
> >>> There is the Tukey window, which I think has a "flat" top.
>
> >>> FIR filter design by window functions is all but obsolete
> >>> after methods like Parks-McClellan were developed. So the
> >>> detailed analysis of window functions is not all that
> >>> interesting these days...
>
> >>> Rune
>
> >> AFAIK, Parks-McClellan, AKA Remez Exchange filters must be verified before
> >> use since it may not not converge to a solution.
>
> > Maybe but you verify by running it - not before. Not a huge cost.
>
> If you are writing a program that designs a filter and then runs it,
> what should the program do if it fails verification?
>
>
>
> >> Windowed design is still needed where predictability and stability is more
> >> important than squeezing the utmost out of every coefficient.
>
> > What predicability and stability do you refer to here? It appears you mean
> > the predictability of being able to achieve a design. P-M is so easy to try
> > that it's always a first step for me. If it fails, then I've only wasted a
> > couple of minutes.
>
> Fine, but for a system that autonomously generates and executes a
> filter, I'll stick with window design.

yeah, i think, even if source code exists for P-McC or similar, if
someone draws a target frequency response (magnitude only, or
magnitude and phase) for positive frequency (and assuming Hermitian
symmetry or real h[n]), that an automated process that iterates the
remez exchange algorithm and checks for convergence, might be a little
icky. i would expect to do it by inverse DFT (with a lot more points
than length of h[n]), and windowing it (probably with Kaiser) to your
length limit. as an automated filter that you draw on the screen, hit
some soft button, and viola - an FIR that hopefully closely follows
your spec to within some constant delay necessary for causality.

but if it's not some rack-mounted real-time box or similar computer
program or plug-in, but an engineering procedure, if the tools are
quick and cheap to run, i see no reason *not* to compare, for a given
FIR length, what you will get from a variety of methods: various
windowed h[n], Least Square fit, Parks-McClellan, possibly an LMS
filter with repeated input having output convergerging to an optimal
solution, something else that hasn't been dreamt up yet.

r b-j

[Jerry Avins]

Mark Borgerding wrote:

...

> If you are writing a program that designs a filter and then runs it,
> what should the program do if it fails verification?
>
>>
>>> Windowed design is still needed where predictability and stability is
>>> more important than squeezing the utmost out of every coefficient.

Most design programs show you the resulting response. One look and
failure is evident.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[John E. Hadstate]

"Jerry Avins" <[email protected]> wrote in message
news:[email protected]...
> Mark Borgerding wrote:
>
> ...
>
>> If you are writing a program that designs a filter and
>> then runs it, what should the program do if it fails
>> verification?
>>
>>>
>>>> Windowed design is still needed where predictability
>>>> and stability is more important than squeezing the
>>>> utmost out of every coefficient.
>
> Most design programs show you the resulting response. One
> look and failure is evident.
>

I think Mark was talking about systems that measure
properties of a real-time signal and then create filters on
the fly to exploit those signals in real-time. If so, he
was correct; windowed filter design is the only way to go.

[robert bristow-johnson]

On Oct 31, 9:32 pm, "John E. Hadstate" <[email protected]> wrote:
>
> I think Mark was talking about systems that measure
> properties of a real-time signal and then create filters on
> the fly to exploit those signals in real-time. If so, he
> was correct; windowed filter design is the only way to go.

well, actually John, i think LMS is another way to go. "measur[ing]
properties of a real-time signal and then creat[ing] filters on the
fly to exploit those signals in real-time" is what LMS filters do,
too. both algs are, essentially, adaptive filters.

r b-j

[John E. Hadstate]

"robert bristow-johnson" <[email protected]> wrote in
message
news:[email protected] oups.com...
> On Oct 31, 9:32 pm, "John E. Hadstate"
> <[email protected]> wrote:
>>
>> I think Mark was talking about systems that measure
>> properties of a real-time signal and then create filters
>> on
>> the fly to exploit those signals in real-time. If so, he
>> was correct; windowed filter design is the only way to
>> go.
>
> well, actually John, i think LMS is another way to go.
> "measur[ing]
> properties of a real-time signal and then creat[ing]
> filters on the
> fly to exploit those signals in real-time" is what LMS
> filters do,
> too. both algs are, essentially, adaptive filters.
>

I probably did not express well what I was thinking. I'm
pretty sure that LMS filters are not useful in the
applications I envisioned.

[Peter K.]

Chris Bore <[email protected]> writes:

> I think in fact Parks McLellan design(s) typically use either MiniMax
> or LMS - depending whether you wish to specify minimum stop-band
> attenuation and maximum pass-band error, or constraints on signal
> energy.

No, the criterion with Parks-McLellan is always minimax. There are
weightings you can apply that emphasize stop band versus the passband.

I'm not sure what you mean by "constraints on signal energy".

> Although, as Parks explains better than I can (in his book, Digital
> Filter Design written with Burrus), in truth the desired approximation
> is a matter of choice and there are other approximations than either
> Chebyshev or least squares. Actually, that book by Parks is I think
> one of the better texts on filter design, although I do not think it
> is for beginners. He discusses several approximations, and also
> discusses window design in the same context as iterative apprximation
> methods.

Ya, Parks is pretty lucid (he's a pretty lucid kinda guy)... though I
agree with the "not for beginners" assessment.

"Traditional" filters (e.g. Butterworth, Tschebitschev, Bessel) also
use design criteria --- just not minimax or least squares (maximally
flat passband / stopband, passband ripple / stopband attenuation, maximally
linear phase).

Ciao,

Peter K.


--
"And he sees the vision splendid
of the sunlit plains extended
And at night the wondrous glory of the everlasting stars."

[Fred Marshall]

"Peter K." <[email protected]> wrote in message
news:[email protected]...
> Chris Bore <[email protected]> writes:
>
>> I think in fact Parks McLellan design(s) typically use either MiniMax
>> or LMS - depending whether you wish to specify minimum stop-band
>> attenuation and maximum pass-band error, or constraints on signal
>> energy.
>
> No, the criterion with Parks-McLellan is always minimax. There are
> weightings you can apply that emphasize stop band versus the passband.
>

And it's pretty easy to make the weights a sequence/function rather than a
constant per band. That's just not built into the standard P-M
implementation. Actually they do it in the differentiator design I believe.
Something like 1/f.

And there can be a reasonable number of equality constraints - like forcing
a zero at a particular frequency in a stop band. Each one uses up one
degree of freedom in the design - so you pay for it in increased ripple.

I took Chris "energy" comment to mean something akin to LMS.

Fred

[SteveSmith]

Look at page 176 in Chapter 9 of my free online DSP book, www.DSPguide.com
This outlines how to implement a flat top window and why you might want t
use it.
Regards,
Steve Smith

[Fred Marshall]

"SteveSmith" <[email protected]> wrote in message
news:[email protected] ...
> Look at page 176 in Chapter 9 of my free online DSP book,
> www.DSPguide.com.
> This outlines how to implement a flat top window and why you might want to
> use it.
> Regards,
> Steve Smith
>
Steve,

I believe that's not what the OP is talking about. He means the temporal
window is flat-topped and not the FT of the window. Thus his reference to a
trapezoidal window. A flat-topped FT of a temporal window as on your p.176
is a bandpass filter, isn't it? Well, I guess so because the context is
spectral analysis.

Fred

[robert bristow-johnson]

On Nov 1, 12:26 pm, "SteveSmith" <[email protected]> wrote:
> Look at page 176 in Chapter 9 of my free online DSP book,www.DSPguide.com.
> This outlines how to implement a flat top window and why you might want to
> use it.
> Regards,
> Steve Smith

hey Steve, it's nice to see you here.

welcome.

r b-j

(we got Steve, we got Rick, we got Tim... when are we gonna start
seeing Alan Oppenheim hanging out here at comp.dsp?)

[Richard Owlett]

Fred Marshall wrote:
> "SteveSmith" <[email protected]> wrote in message
> news:[email protected] ...
>
>>Look at page 176 in Chapter 9 of my free online DSP book,
>>www.DSPguide.com.
>>This outlines how to implement a flat top window and why you might want to
>>use it.
>>Regards,
>>Steve Smith
>>
>
> Steve,
>
> I believe that's not what the OP is talking about. He means the temporal
> window is flat-topped and not the FT of the window. Thus his reference to a
> trapezoidal window. A flat-topped FT of a temporal window as on your p.176
> is a bandpass filter, isn't it? Well, I guess so because the context is
> spectral analysis.
>
> Fred
>

Actually my problem was confusing time domain apples with frequency
domain oranges. I'm gradually getting my conceptions in line with reality.

The key is carefully specifying what I want to accomplish *AND* why.
Sometimes the "why" and the "what" aren't really compatible ;)

[Fred Marshall]

"robert bristow-johnson" <[email protected]> wrote in message
news:[email protected] oups.com...
> On Nov 1, 12:26 pm, "SteveSmith" <[email protected]> wrote:
>> Look at page 176 in Chapter 9 of my free online DSP
>> book,www.DSPguide.com.
>> This outlines how to implement a flat top window and why you might want
>> to
>> use it.
>> Regards,
>> Steve Smith
>
> hey Steve, it's nice to see you here.
>
> welcome.
>
> r b-j
>
> (we got Steve, we got Rick, we got Tim... when are we gonna start
> seeing Alan Oppenheim hanging out here at comp.dsp?)
>

When Don Felder rejoins Eagles?

Fred

[Ron N.]

On Nov 1, 1:14 am, "John E. Hadstate" <[email protected]> wrote:
> "robert bristow-johnson" <[email protected]> wrote in
> messagenews:[email protected] ooglegroups.com...
>
>
>
> > On Oct 31, 9:32 pm, "John E. Hadstate"
> > <[email protected]> wrote:
>
> >> I think Mark was talking about systems that measure
> >> properties of a real-time signal and then create filters
> >> on
> >> the fly to exploit those signals in real-time. If so, he
> >> was correct; windowed filter design is the only way to
> >> go.
>
> > well, actually John, i think LMS is another way to go.
> > "measur[ing]
> > properties of a real-time signal and then creat[ing]
> > filters on the
> > fly to exploit those signals in real-time" is what LMS
> > filters do,
> > too. both algs are, essentially, adaptive filters.
>
> I probably did not express well what I was thinking. I'm
> pretty sure that LMS filters are not useful in the
> applications I envisioned.

One difference is non-linearity, not in the filter
itself, but in how the response varies due to changes
in the spec. Change the spec slightly on a P-M (or
differential evolution, etc.) designed filter, and
it's possible for the shape of the pass/stop band ripple
and/or the pole zero locations to end up looking very
different. Whereas a filter designed by a windowing
method is more likely to have very similar response
curves and pole/zero locations, given a similar specs.

The sudden random change of small "gotcha's" such
as changes in pre-echo delay, etc., are probably
undesirable in some applications.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

[Al Clark]

robert bristow-johnson <[email protected]> wrote in
news:[email protected] oups.com:

> On Nov 1, 12:26 pm, "SteveSmith" <[email protected]> wrote:
>> Look at page 176 in Chapter 9 of my free online DSP
>> book,www.DSPguide.com.
>> This outlines how to implement a flat top window and why you might
>> want to
>> use it.
>> Regards,
>> Steve Smith
>
> hey Steve, it's nice to see you here.
>
> welcome.
>
> r b-j
>
> (we got Steve, we got Rick, we got Tim... when are we gonna start
> seeing Alan Oppenheim hanging out here at comp.dsp?)
>
>

Three engineers in the same group that can write! Thats got to be some kind
of record!

Al Clark
Danville Signal

[Peter K.]

"Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:

> "Peter K." <[email protected]> wrote in message
> news:[email protected]...
> > Chris Bore <[email protected]> writes:
> >
> >> I think in fact Parks McLellan design(s) typically use either MiniMax
> >> or LMS - depending whether you wish to specify minimum stop-band
> >> attenuation and maximum pass-band error, or constraints on signal
> >> energy.
> >
> > No, the criterion with Parks-McLellan is always minimax. There are
> > weightings you can apply that emphasize stop band versus the passband.
> >
>
> And it's pretty easy to make the weights a sequence/function rather than a
> constant per band. That's just not built into the standard P-M
> implementation. Actually they do it in the differentiator design I believe.
> Something like 1/f.
>
> And there can be a reasonable number of equality constraints - like forcing
> a zero at a particular frequency in a stop band. Each one uses up one
> degree of freedom in the design - so you pay for it in increased ripple.
>
> I took Chris "energy" comment to mean something akin to LMS.
>

OK, that makes sense with that spin on it.

Thanks,

Peter K.

--
"And he sees the vision splendid
of the sunlit plains extended
And at night the wondrous glory of the everlasting stars."

[Jerry Avins]

Al Clark wrote:

...

> Three engineers in the same group that can write! Thats got to be some kind
> of record!

Had you written /who/ can write, that might have amounted to four! :-)

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Al Clark]

Jerry Avins <[email protected]> wrote in
news:[email protected]:

> Al Clark wrote:
>
> ...
>
>> Three engineers in the same group that can write! Thats got to be
>> some kind of record!
>
> Had you written /who/ can write, that might have amounted to four! :-)
>
> Jerry

No Jerry, there are clearly only three.

Al

[dbd]

On Nov 1, 6:29 pm, [email protected] (Peter K.) wrote:
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:
> > "Peter K." <[email protected]> wrote in message
> >news:[email protected]...
> > > Chris Bore <[email protected]> writes:
>
> > >> I think in fact Parks McLellan design(s) typically use either MiniMax
> > >> or LMS - depending whether you wish to specify minimum stop-band
> > >> attenuation and maximum pass-band error, or constraints on signal
> > >> energy.
>
> > > No, the criterion with Parks-McLellan is always minimax. There are
> > > weightings you can apply that emphasize stop band versus the passband.
>
> > And it's pretty easy to make the weights a sequence/function rather than a
> > constant per band. That's just not built into the standard P-M
> > implementation. Actually they do it in the differentiator design I believe.
> > Something like 1/f.
>
> > And there can be a reasonable number of equality constraints - like forcing
> > a zero at a particular frequency in a stop band. Each one uses up one
> > degree of freedom in the design - so you pay for it in increased ripple.
>
> > I took Chris "energy" comment to mean something akin to LMS.
>
> OK, that makes sense with that spin on it.
>
> Thanks,
>
> Peter K.
>
> --
..> "And he sees the vision splendid
..> of the sunlit plains extended
..> And at night the wondrous glory of the everlasting stars."

In their 'METEOR' code implementation, Parks et al. added concavity
constraints to the specs that could be selected.

http://citeseer.ist.psu.edu/cache/papers/cs/21365/http:zSzzSzwww.music.princeton.eduzSzclasseszSzmet eor_article.pdf/steiglitz92meteor.pdf

Dale B. Dalrymple
http://dbdimages.com
http://stores.lulu.com/dbd
--
And the bush has friends to meet him, and their kindly voices greet
him
In the murmur of the breezes and the river on its bars,

[Richard Owlett]

Al Clark wrote:

> Jerry Avins <[email protected]> wrote in
> news:[email protected]:
>
>
>>Al Clark wrote:
>>
>> ...
>>
>>
>>>Three engineers in the same group that can write! Thats got to be
>>>some kind of record!
>>
>>Had you written /who/ can write, that might have amounted to four! :-)
>>
>>Jerry
>
>
> No Jerry, there are clearly only three.
>
> Al

The error in original was puntuation and spelling.

Should have been:
Three engineers, in the same group, that can write! That's got to be
some kind of record!

[Mark Borgerding]

Jerry Avins wrote:
> Mark Borgerding wrote:
>
> ...
>
>> If you are writing a program that designs a filter and then runs it,
>> what should the program do if it fails verification?

>>>
>>>> Windowed design is still needed where predictability and stability
>>>> is more important than squeezing the utmost out of every coefficient.
>
> Most design programs show you the resulting response. One look and
> failure is evident.
> Jerry

My point pertains to systems in which the filter must be designed and
executed autonomously. There is no human to whom the resulting response
may be shown. The design method itself must be completely trustworthy
and predictable.


--
Mark Borgerding
3dB Labs, Inc
Innovate. Develop. Deliver.

[Jerry Avins]

Richard Owlett wrote:
> Al Clark wrote:
>
>> Jerry Avins <[email protected]> wrote in
>> news:[email protected]:
>>
>>> Al Clark wrote:
>>>
>>> ...
>>>
>>>
>>>> Three engineers in the same group that can write! Thats got to be
>>>> some kind of record!
>>>
>>> Had you written /who/ can write, that might have amounted to four! :-)
>>>
>>> Jerry
>>
>>
>> No Jerry, there are clearly only three.
>>
>> Al
>
> The error in original was puntuation and spelling.
>
> Should have been:
> Three engineers, in the same group, that can write! That's got to be
> some kind of record!

I don't understand the need for, indeed the appropriateness of, the commas.

The proper pronoun for people is "who", not "that".

Would you write, "There are three plates, on the right side of the
table, that are black? I wouldn't. You probably don't. OTOH, "There were
twelve sheep in the field, all of them black, at least on the right side."

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Jerry Avins]

Mark Borgerding wrote:
> Jerry Avins wrote:
>> Mark Borgerding wrote:
>>
>> ...
>>
>>> If you are writing a program that designs a filter and then runs it,
>>> what should the program do if it fails verification?
>
>>>>
>>>>> Windowed design is still needed where predictability and stability
>>>>> is more important than squeezing the utmost out of every coefficient.
>>
>> Most design programs show you the resulting response. One look and
>> failure is evident.
> > Jerry
>
> My point pertains to systems in which the filter must be designed and
> executed autonomously. There is no human to whom the resulting response
> may be shown. The design method itself must be completely trustworthy
> and predictable.

I missed that a first. John H. cleared that up.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Randy Yates]

Jerry Avins <[email protected]> writes:

> Richard Owlett wrote:
>> Al Clark wrote:
>>
>>> Jerry Avins <[email protected]> wrote in
>>> news:[email protected]:
>>>
>>>> Al Clark wrote:
>>>>
>>>> ...
>>>>
>>>>
>>>>> Three engineers in the same group that can write! Thats got to be
>>>>> some kind of record!
>>>>
>>>> Had you written /who/ can write, that might have amounted to four! :-)
>>>>
>>>> Jerry
>>>
>>>
>>> No Jerry, there are clearly only three.
>>>
>>> Al
>>
>> The error in original was puntuation and spelling.
>>
>> Should have been:
>> Three engineers, in the same group, that can write! That's got to be
>> some kind of record!
>
> I don't understand the need for, indeed the appropriateness of, the commas.
>
> The proper pronoun for people is "who", not "that".
>
> Would you write, "There are three plates, on the right side of the
> table, that are black? I wouldn't. You probably don't. OTOH, "There
> were twelve sheep in the field, all of them black, at least on the
> right side."

I've never understood when one should use a trailing comma in
constructions like this:

I have performed embedded processor development using Motorola, TI,
and Analog Devices microprocessors.

When is the second command appropriate and when isn't it?
--
% Randy Yates % "Ticket to the moon, flight leaves here today
%% Fuquay-Varina, NC % from Satellite 2"
%%% 919-577-9882 % 'Ticket To The Moon'
%%%% <[email protected]> % *Time*, Electric Light Orchestra
http://www.digitalsignallabs.com

[Randy Yates]

Randy Yates <[email protected]> writes:

> When is the second command appropriate and when isn't it?
^^^^^^^
comma!!!
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <[email protected]> % 'Yours Truly, 2095', *Time*, ELO
http://www.digitalsignallabs.com

[Jerry Avins]

Randy Yates wrote:

...

> I have performed embedded processor development using Motorola, TI,
> and Analog Devices microprocessors.
>
> When is the second command appropriate and when isn't it?

I assume you intended "comma", just as I intended "grammar".

Some style manual require the final comma, others forbid it. My tech
writing experience taught me to use it. Ambiguity is the worst form of
poor style in technical documents, and sometimes a list would be
ambiguous without the final comma. Consistency is also important, so I
use it even when the meaning would be clear with out it. Example: We
read stories about Moses, Jacob, Adam and Eve. Did Adam and Eve each
have a story, or was there one story about both? Yes, you can figure it
out, but you shouldn't have to.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Richard Owlett]

Jerry Avins wrote:
> Richard Owlett wrote:
>
>> Al Clark wrote:
>>
>>> Jerry Avins <[email protected]> wrote in
>>> news:[email protected]:
>>>
>>>> Al Clark wrote:
>>>>
>>>> ...
>>>>
>>>>
>>>>> Three engineers in the same group that can write! Thats got to be
>>>>> some kind of record!
>>>>
>>>>
>>>> Had you written /who/ can write, that might have amounted to four! :-)
>>>>
>>>> Jerry
>>>
>>>
>>>
>>> No Jerry, there are clearly only three.
>>>
>>> Al
>>
>>
>> The error in original was puntuation and spelling.
>>
>> Should have been:
>> Three engineers, in the same group, that can write! That's got to be
>> some kind of record!
>
>
> I don't understand the need for, indeed the appropriateness of, the commas.

I think you hit on the key point in your post on "when to use a comma".
You said you did a lot of tech writing. I think my instructors would
class that at the "formal" end of "standard English". I write more
informally - taught to model flow on my conversational style.

In conversation,
An engineer that can write!
seems to have more impact than
An engineer who can write!

As to the commas, "in the same group" seems to be used more
parenthetically than as an adjectival phrase. Thus commas.

As with using commas in lists, a comma can change the meaning.


>
> The proper pronoun for people is "who", not "that".
>
> Would you write, "There are three plates, on the right side of the
> table, that are black? I wouldn't. You probably don't. OTOH, "There were
> twelve sheep in the field, all of them black, at least on the right side."
>
> Jerry

[Al Clark]

Richard Owlett <[email protected]> wrote in
news:[email protected]:

> Jerry Avins wrote:
>> Richard Owlett wrote:
>>
>>> Al Clark wrote:
>>>
>>>> Jerry Avins <[email protected]> wrote in
>>>> news:[email protected]:
>>>>
>>>>> Al Clark wrote:
>>>>>
>>>>> ...
>>>>>
>>>>>
>>>>>> Three engineers in the same group that can write! Thats got to be
>>>>>> some kind of record!
>>>>>
>>>>>
>>>>> Had you written /who/ can write, that might have amounted to four!
>>>>> :-)
>>>>>
>>>>> Jerry
>>>>
>>>>
>>>>
>>>> No Jerry, there are clearly only three.
>>>>
>>>> Al
>>>
>>>
>>> The error in original was puntuation and spelling.
>>>
>>> Should have been:
>>> Three engineers, in the same group, that can write! That's got to be
>>> some kind of record!
>>
>>
>> I don't understand the need for, indeed the appropriateness of, the
>> commas.
>
> I think you hit on the key point in your post on "when to use a
> comma". You said you did a lot of tech writing. I think my instructors
> would class that at the "formal" end of "standard English". I write
> more informally - taught to model flow on my conversational style.
>
> In conversation,
> An engineer that can write!
> seems to have more impact than
> An engineer who can write!
>
> As to the commas, "in the same group" seems to be used more
> parenthetically than as an adjectival phrase. Thus commas.
>
> As with using commas in lists, a comma can change the meaning.
>
>
>>
>> The proper pronoun for people is "who", not "that".
>>
>> Would you write, "There are three plates, on the right side of the
>> table, that are black? I wouldn't. You probably don't. OTOH, "There
>> were twelve sheep in the field, all of them black, at least on the
>> right side."
>>
>> Jerry
>

After Richard's comments about "that" versus "who", I went to
dictionary.com.....

that /ðæt; unstressed ð?t/ Pronunciation Key - Show Spelled
Pronunciation[that; unstressed thuht] Pronunciation Key - Show IPA
Pronunciation pronoun and adjective, plural those; adverb; conjunction
–pronoun
1. (used to indicate a person, thing, idea, state, event, time, remark,
etc., as pointed out or present, mentioned before, supposed to be
understood, or by way of emphasis): That is her mother. After that we saw
each other.
2. (used to indicate one of two or more persons, things, etc., already
mentioned, referring to the one more remote in place, time, or thought;
opposed to this): This is my sister and that's my cousin.

From my reading, "that" is acceptable.

I'm still not claiming that I can write.

Al Clark
Danville Signal Processing

[Jerry Avins]

Richard Owlett wrote:

...

> In conversation,
> An engineer that can write!
> seems to have more impact than
> An engineer who can write!

"An engineer what writes" has more impact yet. As the hammer said to the
tinker, what kind of impact do you want to make?

> As to the commas, "in the same group" seems to be used more
> parenthetically than as an adjectival phrase. Thus commas.

If it would seem silly with parentheses, don't use commas.

> As with using commas in lists, a comma can change the meaning.

Indeed. "Pardon, impossible to be executed" vs. "Pardon impossible, to
be executed."

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Jerry Avins]

Al Clark wrote:

...

> After Richard's comments about "that" versus "who", I went to
> dictionary.com.....
>
> that ... pronoun
> 1. (used to indicate a person, thing, idea, state, event, time, remark,
> etc., as pointed out or present, mentioned before, supposed to be
> understood, or by way of emphasis): That is her mother. After that we saw
> each other.
> 2. (used to indicate one of two or more persons, things, etc., already
> mentioned, referring to the one more remote in place, time, or thought;
> opposed to this): This is my sister and that's my cousin.
>
> From my reading, "that" is acceptable.
>
> I'm still not claiming that I can write.

"Used to indicate" may be the key. The sentence expanded somewhat is
This [person] is my sister and that [person's] my cousin.
That's perfectly fine. Referring to your wife, unless you choose to
portray her as an object, you wouldn't say "That is the woman that bore
my children." The first that and the second stand in different relation
to her. Do you see the difference?

I said that that that that that man used was improper. :-)

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

[Richard Owlett]

Jerry Avins wrote:

> Richard Owlett wrote:
>
> ...
>
>> In conversation,
>> An engineer that can write!
>> seems to have more impact than
>> An engineer who can write!
>
>
> "An engineer what writes" has more impact yet. As the hammer said to the
> tinker, what kind of impact do you want to make?
>
>> As to the commas, "in the same group" seems to be used more
>> parenthetically than as an adjectival phrase. Thus commas.
>
>
> If it would seem silly with parentheses, don't use commas.

Yeah. I read it as being a parenthetic comment. Therefor used commas.
Use of "(" and ")" would have been too strong. So there are at least
three shades of interpretation of sentence depending on how its punctuated.

As to "that" vs "who", I don't see a real problem with using "that" to
refer back to a collective noun even if it refers to a collection of
persons.

>
>> As with using commas in lists, a comma can change the meaning.
>
>
> Indeed. "Pardon, impossible to be executed" vs. "Pardon impossible, to
> be executed."
>
> Jerry

[Peter K.]

Jerry Avins <[email protected]> writes:

>
> I said that that that that that man used was improper. :-)
>

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

Ciao,

Peter K.

--
"And he sees the vision splendid
of the sunlit plains extended
And at night the wondrous glory of the everlasting stars."

[Rick Lyons]

On Mon, 29 Oct 2007 04:46:42 -0700, Chris Bore <[email protected]>
wrote:

>>FIR filter design by window functions is all but obsolete
>>after methods like Parks-McClellan were developed. So the
>>detailed analysis of window functions is not all that
>>interesting these days...
>
>Umm. Parks-McLellan gives the 'best' filter if you mean by 'best',
>'least mean squares approximation'.
>Other iterative filter design methods each aim for their own type of
>'best' approximation, but I do not think they necessarily make FIR
>window filter design obsolete or uninteresting. Sometimes we want some
>other approximation. Or sometimes we want a filter whose shape can be
>processed analytically rather than numerically.
>
>And, the choice of appropriate window to apply before an FFT is not
>quite the same problem as using a window to design an FIR filter.
>
>Chris

Hi Chris (hope all is well)

Did ya' know that before Parks and Mclellan
proposed their filter design alogrithm there were
only two known ways to design FIR filters:
(1) the window design method, and (2) a method
called "frequency sampling filters"?

With those two methods, however, a designer could
never be sure that their design used the minimum
number of filter coefficients to meet their
desired filter specifications. Then along came
the revolutionary Parks & McClellan design method.
(In the early 70s, I think.)

The interesting thing is that when Parks & McClellan
initially tried to have their manuscript published
describing their design method, their manuscript
was REJECTED! The editors of some publication
(I forget which one) thought that the problem
Parks & McClellan had solved was actually impossible
to solve. Ha ha.

See Ya',
[-Rick-]

[Rick Lyons]

On Thu, 01 Nov 2007 18:52:53 -0000, robert bristow-johnson
<[email protected]> wrote:

>On Nov 1, 12:26 pm, "SteveSmith" <[email protected]> wrote:
>> Look at page 176 in Chapter 9 of my free online DSP book,www.DSPguide.com.
>> This outlines how to implement a flat top window and why you might want to
>> use it.
>> Regards,
>> Steve Smith
>
>hey Steve, it's nice to see you here.
>
>welcome.
>
>r b-j

Hi R B-J,
I agree. I was tickled to see that Steve
was posting here recently. I've never met Steve
but I'll say this, when Steve talks, I'll listen.

[-Rick-]

[Rick Lyons]

On Thu, 01 Nov 2007 23:20:28 -0400, Jerry Avins <[email protected]> wrote:

>Al Clark wrote:
>
> ...
>
>> Three engineers in the same group that can write! Thats got to be some kind
>> of record!
>
>Had you written /who/ can write, that might have amounted to four! :-)
>
>Jerry

Ah. English is such a devilish language.
Both in grammar and pronunciation.

The letter combination "ough" can be pronounced
in nine different ways. The following sentence
contains them all:

"A rough-coated, dough-faced, thoughtful ploughman
strode through the streets of Scarborough; after
falling into a slough, he coughed and hiccoughed."

[-Rick-]