FPGA Central

Hi,

I'm implementing a HT with sampling freq 2 Mhz to convert a real
signal to complex.. The required passband goes down all the way to 50
hz. I have a couple of questions which hopefully the experts can give
me some advice. First of all. to get the required frequency response
and to keep the passband ripple as low as possible, I need a large
number of taps and this uses a lot of resources on an FPGA. Is there a
quick and dirty method to implement a HT which will reduce the number
of resources required? Would running the input signal through a simple
delay line to get the 90 degree phase shift work? I've thought about
it and I don't think it would because I don't think it would filter
out the negative frequencies but I would like confirmation of this or
not.


Tapping output from the centre tap...Can this output be just the input
delayed or does it have to be the result of the input convolved with
half the filter coefficients.

Many Thanks
Bob Carter

On Thu, 11 Jun 2009 07:39:22 -0700, Bob wrote:

> Hi,
>
> I'm implementing a HT with sampling freq 2 Mhz to convert a real signal
> to complex.. The required passband goes down all the way to 50 hz. I
> have a couple of questions which hopefully the experts can give me some
> advice. First of all. to get the required frequency response and to keep
> the passband ripple as low as possible, I need a large number of taps
> and this uses a lot of resources on an FPGA. Is there a quick and dirty
> method to implement a HT which will reduce the number of resources
> required? Would running the input signal through a simple delay line to
> get the 90 degree phase shift work? I've thought about it and I don't
> think it would because I don't think it would filter out the negative
> frequencies but I would like confirmation of this or not.
>
>
> Tapping output from the centre tap...Can this output be just the input
> delayed or does it have to be the result of the input convolved with
> half the filter coefficients.

It's hardly quick and dirty, but you should consider using some IIR
stages instead of starting with the assumption of an all-FIR transformer.

You did not say what bandwidth you need good phase shifting over, nor
what sort of phase precision -- both of these have a profound effect on
filter complexity. If, for instance, you only need 90 degrees of phase
shift between 50 and 60Hz, you should be able to filter, decimate,
transform, and if necessary resample with a lot less math than if you had
to have near-perfect phase shifting from 50Hz to 500000.

Just delaying one signal isn't going to give you a good phase shift over
a very wide band.

"Tapping output from the center tap?" I think you mean you're delaying
the un-transformed signal? If so, you just want it delayed -- you
certainly don't want to run it through half your HT filter.

--
www.wescottdesign.com

On 11 June, 16:13, Tim Wescott <t...@seemywebsite.com> wrote:
> On Thu, 11 Jun 2009 07:39:22 -0700, Bob wrote:
> > Hi,
>
> > I'm implementing a HT with sampling freq 2 Mhz to convert a real signal
> > to complex.. The required passband goes down all the way to 50 hz. I
> > have a couple of questions which hopefully the experts can give me some
> > advice. First of all. to get the required frequency response and to keep
> > the passband ripple as low as possible, I need a large number of taps
> > and this uses a lot of resources on an FPGA. Is there a quick and dirty
> > method to implement a HT which will reduce the number of resources
> > required? Would running the input signal through a simple delay line to
> > get the 90 degree phase shift work? I've thought about it and I don't
> > think it would because I don't think it would filter out the negative
> > frequencies but I would like confirmation of this or not.
>
> > Tapping output from the centre tap...Can this output be just the input
> > delayed or does it have to be the result of the input convolved with
> > half the filter coefficients.
>
> It's hardly quick and dirty, but you should consider using some IIR
> stages instead of starting with the assumption of an all-FIR transformer.
>
> You did not say what bandwidth you need good phase shifting over, nor
> what sort of phase precision -- both of these have a profound effect on
> filter complexity. *If, for instance, you only need 90 degrees of phase
> shift between 50 and 60Hz, you should be able to filter, decimate,
> transform, and if necessary resample with a lot less math than if you had
> to have near-perfect phase shifting from 50Hz to 500000.
>
> Just delaying one signal isn't going to give you a good phase shift over
> a very wide band.
>
> "Tapping output from the center tap?" *I think you mean you're delaying
> the un-transformed signal? *If so, you just want it delayed -- you
> certainly don't want to run it through half your HT filter.
>
> --www.wescottdesign.com

Hi Tim,

I'm afraid the bandwidth is wideband... 50 Hz all the way to 700000
Hz. Regarding delaying the un-transformed signal...yep that is what
I'm doing. I'm appling a sine wave at the input and tapping it off the
middle delay..so I see a nice clean sine wave. The output is a little
distorted but the phase shift looks correct though.

Bob

On Jun 11, 11:30*am, Bob <sten...@yahoo.com> wrote:
>
> > > I'm implementing a HT with sampling freq 2 Mhz to convert a real signal
> > > to complex.. The required passband goes down all the way to 50 hz.

....

> I'm afraid the bandwidth is wideband... 50 Hz all the way to 700000 Hz.

Whoa, Nellie!!!

okay, so yer gonna have a reasonably flat passband from 700 kHz down
to 50 Hz, *then* the filter magnitude must necessarily drop to 0 (or -
inf dB) at DC and pop back up to the flat level at -50 Hz where it
stays reasonably flat until -700 kHz.

in audio, when i've done an HT, it was a bitch just to have it flat
from about 80 Hz to nearly 22 kHz. it's gonna be a *very* long FIR.

> Regarding delaying the un-transformed signal...yep that is what
> I'm doing. I'm appling a sine wave at the input and tapping it off the
> middle delay..so I see a nice clean sine wave. The output is a little
> distorted but the phase shift looks correct though.

so how long is your FIR? you *could* use halfband symmetry, but the
50 Hz spec on your bottom will translate to a Nyquist-50Hz spec on the
top, which is probably better than you need.

tough spec.

r b-j

>On Jun 11, 11:30=A0am, Bob <sten...@yahoo.com> wrote:
>>
>> > > I'm implementing a HT with sampling freq 2 Mhz to convert a rea
sign=
>al
>> > > to complex.. The required passband goes down all the way to 50 hz.
>
>...
>
>> I'm afraid the bandwidth is wideband... 50 Hz all the way to 70000
Hz.
>
>Whoa, Nellie!!!
>
>okay, so yer gonna have a reasonably flat passband from 700 kHz down
>to 50 Hz, *then* the filter magnitude must necessarily drop to 0 (or -
>inf dB) at DC and pop back up to the flat level at -50 Hz where it
>stays reasonably flat until -700 kHz.
>
>in audio, when i've done an HT, it was a bitch just to have it flat
>from about 80 Hz to nearly 22 kHz. it's gonna be a *very* long FIR.
>
>> Regarding delaying the un-transformed signal...yep that is what
>> I'm doing. I'm appling a sine wave at the input and tapping it off the
>> middle delay..so I see a nice clean sine wave. The output is a little
>> distorted but the phase shift looks correct though.
>
>so how long is your FIR? you *could* use halfband symmetry, but the
>50 Hz spec on your bottom will translate to a Nyquist-50Hz spec on the
>top, which is probably better than you need.
>
>tough spec.

There are ways to recast a Hilbert transform as an IIR, which can reduc
the number of calculations, but the word length of the calculations become
wacky. I don't think the overall computational complexity is any better.

This is a problem in power measurement (I mean real power - the 50Hz/60H
stuff you pay utilities cash for). To produce a genuine reactive powe
measurement, with all the harmonics handled correctly, you really want
Hilbert transform that's 0.05% flat in response and 90+-0.02 degrees i
phase over the range 45Hz to a few kHz. Its a pain.

Most applications of Hilbert are in comms, and those are prett
straightforward. A modest length FIR based Hilbert transform will do 80% o
the band pretty well. A modest amount of ripple, and a minor phase erro
can also be tolerated, without significant performance degradation. Yo
just keep away from DC, sample a bit faster, and chop the ends of the ban
off. :-)

Steve

On 12 June, 01:35, robert bristow-johnson <r...@audioimagination.com>
wrote:
> On Jun 11, 11:30*am, Bob <sten...@yahoo.com> wrote:
>
>
>
> > > > I'm implementing a HT with sampling freq 2 Mhz to convert a real signal
> > > > to complex.. The required passband goes down all the way to 50 hz.
>
> ...
>
> > I'm afraid the bandwidth is wideband... 50 Hz all the way to 700000 Hz.
>
> Whoa, Nellie!!!
>
> okay, so yer gonna have a reasonably flat passband from 700 kHz down
> to 50 Hz, *then* the filter magnitude must necessarily drop to 0 (or -
> inf dB) at DC and pop back up to the flat level at -50 Hz where it
> stays reasonably flat until -700 kHz.
>
> in audio, when i've done an HT, it was a bitch just to have it flat
> from about 80 Hz to nearly 22 kHz. *it's gonna be a *very* long FIR.
>
> > Regarding delaying the un-transformed signal...yep that is what
> > I'm doing. I'm appling a sine wave at the input and tapping it off the
> > middle delay..so I see a nice clean sine wave. The output is a little
> > distorted but the phase shift looks correct though.
>
> so how long is your FIR? *you *could* use halfband symmetry, but the
> 50 Hz spec on your bottom will translate to a Nyquist-50Hz spec on the
> top, which is probably better than you need.
>
> tough spec.
>
> r b-j


There is no way on earth I can meet that spec using a conventional HT.
If I change the passband to 10KHz to 990 KHz and have it symmetrical,
then I begin to see a decent result using approx 100 taps...which I
could implement on an FPGA. However, I need to get the lower edge of
the passband down closer to 50 Hz. Is there any other way of achieving
the same effect as a HT for baseband signals?

Thanks
Bob

On Jun 11, 10:39*am, Bob <sten...@yahoo.com> wrote:
> Hi,
>
> I'm implementing a HT with sampling freq 2 Mhz to convert a real
> signal to complex.. The required passband goes down all the way to 50
> hz. I have a couple of questions which hopefully the experts can give
> me some advice. First of all. to get the required frequency response
> and to keep the passband ripple as low as possible, I need a large
> number of taps and this uses a lot of resources on an FPGA. Is there a
> quick and dirty method to implement a HT which will reduce the number
> of resources required? Would running the input signal through a simple
> delay line to get the 90 degree phase shift work? I've thought about
> it and I don't think it would because I don't think it would filter
> out the negative frequencies but I would like confirmation of this or
> not.
>
> Tapping output from the centre tap...Can this output be just the input
> delayed or does it have to be the result of the input convolved with
> half the filter coefficients.
>
> Many Thanks
> Bob Carter

Hello Bob,

You have one set of crazy specs! I assume you are trying to make an
analytic signal, so how about subdividing your original signal into
bands using quadrature mirror filters with appropriate decimation
after each bandsplit, and then forming each of these band outputs into
analytic signals. Then when appropriately combined (after applying
proper delays and interpolation) you can make your wideband analytic
signal. But this may take several FPGAs. I don't think there is an
easy answer to your problem without somehow relaxing your spec. Does
your signal processing really require such a bandwidth all at the same
time? Or does your process use a smaller bandwidth but just needs to
be frequency agile? If you can reduce the bandwidth, then your Hilbert
problem gets simpler. For efficiently making analytic signals I have
an article that describes a way to do it that will be availible on
July 1st in the Signal Processing Magazine.

FWIW,
Clay

On Jun 12, 5:22 am, Bob <sten...@yahoo.com> wrote:
> On 12 June, 01:35, robert bristow-johnson <r...@audioimagination.com>
> wrote:
>
> > On Jun 11, 11:30 am, Bob <sten...@yahoo.com> wrote:
>
> > > > > I'm implementing a HT with sampling freq 2 Mhz to convert a real signal
> > > > > to complex.. The required passband goes down all the way to 50 hz.
>
> > ...
>
> > > I'm afraid the bandwidth is wideband... 50 Hz all the way to 700000 Hz.
>
> > Whoa, Nellie!!!
>
....
>
> > so how long is your FIR? you *could* use halfband symmetry, but the
> > 50 Hz spec on your bottom will translate to a Nyquist-50Hz spec on the
> > top, which is probably better than you need.
>
> > tough spec.
....
>
> There is no way on earth I can meet that spec using a conventional HT.

no shit. not without a lot of taps.

> If I change the passband to 10KHz to 990 KHz and have it symmetrical,
> then I begin to see a decent result using approx 100 taps...which I
> could implement on an FPGA.

with halfband symmetry, those 100 taps are interlaced with zero-valued
taps, so the "reach" of the impulse response is about 200 taps. when
you give up on symmetry, you lose those zero taps and then you have to
pay for computing them. also, while this makes little difference with
a DSP, in an FPGA you can take advantage of symmetry in the IR and
have half (again) as many multiplications even though you still have
the same number of memory accesses and additions.

> However, I need to get the lower edge of
> the passband down closer to 50 Hz. Is there any other way of achieving
> the same effect as a HT for baseband signals?

without bumping your signal spectrum up by (10000-50) Hz (and how're
you gonna do that without an HT?) and bumping it back down, i dunno.
maybe the old fashioned way we ham operators used to do it in single-
sideband (SSB) with "mixers" and crystal-lattice filters. you'll need
some pretty sharp IIR filters. it might not work so well. i dunno.

it's a damn tough spec.

r b-j

On 12 June, 23:42, robert bristow-johnson <r...@audioimagination.com>
wrote:
> On Jun 12, 5:22 am, Bob <sten...@yahoo.com> wrote:
>
>
>
> > On 12 June, 01:35, robert bristow-johnson <r...@audioimagination.com>
> > wrote:
>
> > > On Jun 11, 11:30 am, Bob <sten...@yahoo.com> wrote:
>
> > > > > > I'm implementing a HT with sampling freq 2 Mhz to convert a real signal
> > > > > > to complex.. The required passband goes down all the way to 50 hz.
>
> > > ...
>
> > > > I'm afraid the bandwidth is wideband... 50 Hz all the way to 700000Hz.
>
> > > Whoa, Nellie!!!
>
> ...
>
> > > so how long is your FIR? *you *could* use halfband symmetry, but the
> > > 50 Hz spec on your bottom will translate to a Nyquist-50Hz spec on the
> > > top, which is probably better than you need.
>
> > > tough spec.
> ...
>
> > There is no way on earth I can meet that spec using a conventional HT.
>
> no shit. *not without a lot of taps.
>
> > If I change the passband to 10KHz to 990 KHz and have it symmetrical,
> > then I begin to see a decent result using approx 100 taps...which I
> > could implement on an FPGA.
>
> with halfband symmetry, those 100 taps are interlaced with zero-valued
> taps, so the "reach" of the impulse response is about 200 taps. *when
> you give up on symmetry, you lose those zero taps and then you have to
> pay for computing them. *also, while this makes little difference with
> a DSP, in an FPGA you can take advantage of symmetry in the IR and
> have half (again) as many multiplications even though you still have
> the same number of memory accesses and additions.
>

A halfband HT...hmm....didn't know such a beast existed...just
interlace the coeffs with zeros you say...what happens with the
sampling freq...do I double it? I've implemented half bands before to
good effect and also taken advantage of IR symmetry to reduce logic
count on FPGAs so that's an interesting possibility.

> > However, I need to get the lower edge of
> > the passband down closer to 50 Hz. Is there any other way of achieving
> > the same effect as a HT *for baseband signals?
>
> without bumping your signal spectrum up by (10000-50) Hz (and how're
> you gonna do that without an HT?) and bumping it back down, i dunno.
> maybe the old fashioned way we ham operators used to do it in single-
> sideband (SSB) with "mixers" and crystal-lattice filters. *you'll need
> some pretty sharp IIR filters. *it might not work so well. *i dunno.

Was thinking of moving up the spectrum and then mixing back down
again, but that brings its own problems as you've alluded to above.
May have to go down this route yet.
>
> it's a damn tough spec.

Let's just say...It a challenging one !!

>
> r b-j

On 12 June, 16:00, Clay <c...@claysturner.com> wrote:
> On Jun 11, 10:39*am, Bob <sten...@yahoo.com> wrote:
>
>
>
> > Hi,
>
> > I'm implementing a HT with sampling freq 2 Mhz to convert a real
> > signal to complex.. The required passband goes down all the way to 50
> > hz. I have a couple of questions which hopefully the experts can give
> > me some advice. First of all. to get the required frequency response
> > and to keep the passband ripple as low as possible, I need a large
> > number of taps and this uses a lot of resources on an FPGA. Is there a
> > quick and dirty method to implement a HT which will reduce the number
> > of resources required? Would running the input signal through a simple
> > delay line to get the 90 degree phase shift work? I've thought about
> > it and I don't think it would because I don't think it would filter
> > out the negative frequencies but I would like confirmation of this or
> > not.
>
> > Tapping output from the centre tap...Can this output be just the input
> > delayed or does it have to be the result of the input convolved with
> > half the filter coefficients.
>
> > Many Thanks
> > Bob Carter
>
> Hello Bob,
>
> You have one set of crazy specs! I assume you are trying to make an
> analytic signal, so how about subdividing your original signal into
> bands using quadrature mirror filters with appropriate decimation
> after each bandsplit, and then forming each of these band outputs into
> analytic signals. Then when appropriately combined (after applying
> proper delays and interpolation) you can make your wideband analytic
> signal. But this may take several FPGAs. I don't think there is an
> easy answer to your problem without somehow relaxing your spec. Does
> your signal processing really require such a bandwidth all at the same
> time? Or does your process use a smaller bandwidth but just needs to
> be frequency agile? If you can reduce the bandwidth, then your Hilbert
> problem gets simpler. For efficiently making analytic signals I have
> an article that describes a way to do it that will be availible on
> July 1st in the Signal Processing Magazine.
>
> FWIW,
> Clay

Hi Clay,

Yeah...trying to make an analytic signal, which is turning out to be a
pain in the analytic area. The quadrature mirror filters idea would
take up a lot of logic on the chip, so I'd rather not go down that
road. It also looks to be a quite complex task and I'll have the usual
time pressures to contend with. I'm currently investigating if I can
relax the bandwidth requirements and R.B.J. has thrown up some
interesting possibilities as well. However, I'm certainly looking
forward to having a read of your article....any chance of a
preview ???

Regards
Bob

On Jun 11, 9:39*am, Bob <sten...@yahoo.com> wrote:
> Hi,
>
> I'm implementing a HT with sampling freq 2 Mhz to convert a real
> signal to complex.. The required passband goes down all the way to 50
> hz. I have a couple of questions which hopefully the experts can give
> me some advice. First of all. to get the required frequency response
> and to keep the passband ripple as low as possible, I need a large
> number of taps and this uses a lot of resources on an FPGA. Is there a
> quick and dirty method to implement a HT which will reduce the number
> of resources required? Would running the input signal through a simple
> delay line to get the 90 degree phase shift work? I've thought about
> it and I don't think it would because I don't think it would filter
> out the negative frequencies but I would like confirmation of this or
> not.
>
> Tapping output from the centre tap...Can this output be just the input
> delayed or does it have to be the result of the input convolved with
> half the filter coefficients.
>
> Many Thanks
> Bob Carter

Can you do quadrature re-sampling?

On Jun 14, 11:22*am, "wazerf...@gmail.com" <wazerf...@gmail.com>
wrote:
> On Jun 11, 9:39*am, Bob <sten...@yahoo.com> wrote:
>
> > I'm implementing a HT with sampling freq 2 Mhz to convert a real
> > signal to complex.. The required passband goes down all the way to 50
> > hz.
....
>
> Can you do quadrature re-sampling?

ooookay. what exactly is it and how does that speak to solution to
the problem and not the desired consequence of the solution?

r b-j

On Jun 13, 6:08*pm, Bob <sten...@yahoo.com> wrote:
> On 12 June, 16:00, Clay <c...@claysturner.com> wrote:
>
>
>
>
>
> > On Jun 11, 10:39*am, Bob <sten...@yahoo.com> wrote:
>
> > > Hi,
>
> > > I'm implementing a HT with sampling freq 2 Mhz to convert a real
> > > signal to complex.. The required passband goes down all the way to 50
> > > hz. I have a couple of questions which hopefully the experts can give
> > > me some advice. First of all. to get the required frequency response
> > > and to keep the passband ripple as low as possible, I need a large
> > > number of taps and this uses a lot of resources on an FPGA. Is there a
> > > quick and dirty method to implement a HT which will reduce the number
> > > of resources required? Would running the input signal through a simple
> > > delay line to get the 90 degree phase shift work? I've thought about
> > > it and I don't think it would because I don't think it would filter
> > > out the negative frequencies but I would like confirmation of this or
> > > not.
>
> > > Tapping output from the centre tap...Can this output be just the input
> > > delayed or does it have to be the result of the input convolved with
> > > half the filter coefficients.
>
> > > Many Thanks
> > > Bob Carter
>
> > Hello Bob,
>
> > You have one set of crazy specs! I assume you are trying to make an
> > analytic signal, so how about subdividing your original signal into
> > bands using quadrature mirror filters with appropriate decimation
> > after each bandsplit, and then forming each of these band outputs into
> > analytic signals. Then when appropriately combined (after applying
> > proper delays and interpolation) you can make your wideband analytic
> > signal. But this may take several FPGAs. I don't think there is an
> > easy answer to your problem without somehow relaxing your spec. Does
> > your signal processing really require such a bandwidth all at the same
> > time? Or does your process use a smaller bandwidth but just needs to
> > be frequency agile? If you can reduce the bandwidth, then your Hilbert
> > problem gets simpler. For efficiently making analytic signals I have
> > an article that describes a way to do it that will be availible on
> > July 1st in the Signal Processing Magazine.
>
> > FWIW,
> > Clay
>
> Hi Clay,
>
> Yeah...trying to make an analytic signal, which is turning out to be a
> pain in the analytic area. The quadrature mirror filters idea would
> take up a lot of logic on the chip, so I'd rather not go down that
> road. It also looks to be a quite complex task and I'll have the usual
> time pressures to contend with. I'm currently investigating if I can
> relax the bandwidth requirements and R.B.J. has thrown up some
> interesting possibilities as well. However, I'm certainly looking
> forward to having a read of your article....any chance of a
> preview ???
>
> Regards
> Bob- Hide quoted text -
>
> - Show quoted text -

I'm afraid it would be poor form to offer up a detailed preview of the
article before the publisher gets it out. But it does allow for
cutting the number of taps in half and the method has nearly linear
phase.

Clay

In article <4c3b3c23-b833-461c-877e-
[email protected]>, [email protected] says...
>
>
>Hi,
>
>I'm implementing a HT with sampling freq 2 Mhz to convert a real
>signal to complex.. The required passband goes down all the way to 50
>hz. I have a couple of questions which hopefully the experts can give
>me some advice. First of all. to get the required frequency response
>and to keep the passband ripple as low as possible, I need a large
>number of taps and this uses a lot of resources on an FPGA. Is there a
>quick and dirty method to implement a HT which will reduce the number
>of resources required? Would running the input signal through a simple
>delay line to get the 90 degree phase shift work? I've thought about
>it and I don't think it would because I don't think it would filter
>out the negative frequencies but I would like confirmation of this or
>not.
>
>
>Tapping output from the centre tap...Can this output be just the input
>delayed or does it have to be the result of the input convolved with
>half the filter coefficients.

Fast convolution comes to mind. The big challenge with a filter like
this is computing the tap weights (if you want minimax result) because
the MPR algorithm tends to break down when more than a few thousand taps
are computed.

I have done quick and dirty wideband HTs by doing FFTs on large blocks
(~64000 samples), swapping the real and imaginary parts, negating the
new imaginary part, and doing an IFFT. I threw away about 3000 samples
at each end and crossfaded between blocks. When used for SSB modulation,
results were surprisingly good (unwanted sideband suppression was
somewhere better than -80 dB IIRC) even though the technique does not
not meet the strict criteria for overlap and add.

> > On 12 June, 01:35, robert bristow-johnson <r...@audioimagination.com>
> > wrote:
>
> with halfband symmetry, those 100 taps are interlaced with zero-valued
> taps, so the "reach" of the impulse response is about 200 taps. *when
> you give up on symmetry, you lose those zero taps and then you have to
> pay for computing them. *also, while this makes little difference with
> a DSP, in an FPGA you can take advantage of symmetry in the IR and
> have half (again) as many multiplications even though you still have
> the same number of memory accesses and additions.

Another trick with halfband filters that may or may not help...design
a
sub-spec half-band filter and modulate it by one sinusoid with a phase
of -pi/4
and another with a phase of pi/4. This will give you two "Hilbert"
transformers
that are -45 degrees and + 45 degrees (i.e. still 90 degrees out of
phase).
The advantage of doing it this way is that the amplitude response of
the two
filters are identical. For some applications (e.g. magnitude
estimation) the
problem isn't the ripple, it is the mismatched amplitude response
between the
I and Q path...

Darrell

P.S. There is a bit more to it since you need to ensure the center tap
is
sqrt(2)/2, and if this is something you are interested in I'll post
the details.

Darrell <[email protected]> wrote in news:276159ca-f1ec-42f4-b155-
[email protected]:

>> > On 12 June, 01:35, robert bristow-johnson <r...@audioimagination.com>
>> > wrote:
>>
>> with halfband symmetry, those 100 taps are interlaced with zero-valued
>> taps, so the "reach" of the impulse response is about 200 taps. *when
>> you give up on symmetry, you lose those zero taps and then you have to
>> pay for computing them. *also, while this makes little difference with
>> a DSP, in an FPGA you can take advantage of symmetry in the IR and
>> have half (again) as many multiplications even though you still have
>> the same number of memory accesses and additions.
>
> Another trick with halfband filters that may or may not help...design
> a
> sub-spec half-band filter and modulate it by one sinusoid with a phase
> of -pi/4
> and another with a phase of pi/4. This will give you two "Hilbert"
> transformers
> that are -45 degrees and + 45 degrees (i.e. still 90 degrees out of
> phase).
> The advantage of doing it this way is that the amplitude response of
> the two
> filters are identical. For some applications (e.g. magnitude
> estimation) the
> problem isn't the ripple, it is the mismatched amplitude response
> between the
> I and Q path...
>
> Darrell
>
> P.S. There is a bit more to it since you need to ensure the center tap
> is
> sqrt(2)/2, and if this is something you are interested in I'll post
> the details.
>

Clay Turner's excellent article discusses this in the current IEEE Signal
Processing Magazine which I received on Wednesday.

Al Clark
Danville Signal

On Jun 19, 7:12*pm, Al Clark <acl...@danvillesignal.com> wrote:
>
> Clay Turner's excellent article discusses this in the current IEEE Signal
> Processing Magazine which I received on Wednesday.

Funny! I haven't received my copy yet but I'll be sure to look for
it. I was
trying to remember where I first learned the trick, and best I could
recall
it was either this newsgroup or Frerking's book. I guess it must have
been Clay :-).

Darrell