FPGA Central

Hi all,
I have a questions regarding FIR filter length. Usually, as per
formulae from Kaiser or Hermann, it is only a function of passband/
stopband attenuations and transition band-width. However, in practical
world would the transition bandwidth itself not a function of the
filter cutoff frequency?

For example, with 48K sampling frequency, if the filter cutoff is at
5000Hz, a transition BW of 500Hz probably can be considered
acceptable. However, if the filter cutoff is at 100Hz, I would rather
limit the transition BW till the next octave -- 200Hz, not till
100+500Hz. So given the same filter length (and hence passband/
stopband attenuations and transition BW) a filter at 100Hz would
perform worse compared to a filter at 5000Hz. If I want similar
results at both frequencies, then lesser the cutoff frequency, greater
should be the filter length.

Does this appear right?

Thanks,

[email protected] wrote:
> Hi all,
> I have a questions regarding FIR filter length. Usually, as per
> formulae from Kaiser or Hermann, it is only a function of passband/
> stopband attenuations and transition band-width. However, in practical
> world would the transition bandwidth itself not a function of the
> filter cutoff frequency?
>
> For example, with 48K sampling frequency, if the filter cutoff is at
> 5000Hz, a transition BW of 500Hz probably can be considered
> acceptable. However, if the filter cutoff is at 100Hz, I would rather
> limit the transition BW till the next octave -- 200Hz, not till
> 100+500Hz. So given the same filter length (and hence passband/
> stopband attenuations and transition BW) a filter at 100Hz would
> perform worse compared to a filter at 5000Hz. If I want similar
> results at both frequencies, then lesser the cutoff frequency, greater
> should be the filter length.
>
> Does this appear right?

The filter length in samples -- the delay through the filter -- must be
comparable the lowest period it is to influence and to the reciprocal of
the smallest transition time. The degree to which a given length can be
used for both purposes or whether the lengths so estimated must be added
varies with details in a way that I don't understand.

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

On Aug 28, 12:53 pm, matcho_pla...@yahoo.com wrote:
> Hi all,
> I have a questions regarding FIR filter length. Usually, as per
> formulae from Kaiser or Hermann, it is only a function of passband/
> stopband attenuations and transition band-width. However, in practical
> world would the transition bandwidth itself not a function of the
> filter cutoff frequency?

it would get longer with a lower cutoff frequency *if* the transition
bandwidth was reduced along with the lower cutoff, which it would if
the ostensible "Q" was about constant. i.e. if the appearace of the
filter frequency response, on a log-frequency graph, appeared the same
except for being scooted a little to the left, then the FIR would be
longer. but scooting a frequency response to the left on a log-
frequency scale, not only reduces the cutoff frequency but also
reduces the transition bandwidth and because of that, the FIR must be
longer. it is still a function of passband/stopband attenuations and
transition bandwidth. lowering the cutoff (whether Hz or radians/
sample) while retaining a constant transition bandwidth (however it's
defined but measured in the same Hz or radians/sample) will likely not
increase the FIR length much.

r b-j

[email protected] wrote:


> I have a questions regarding FIR filter length. Usually, as per
> formulae from Kaiser or Hermann, it is only a function of passband/
> stopband attenuations and transition band-width. However, in practical
> world would the transition bandwidth itself not a function of the
> filter cutoff frequency?

Rabiner derived a formula for the estimated length of FIR filter:

http://www.appsig.com/products/tn070.htm#sizing

It is a function of all above mentioned parameters.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

<[email protected]> a écrit dans le message de news:
[email protected] m...
> Hi all,
> I have a questions regarding FIR filter length. Usually, as per
> formulae from Kaiser or Hermann, it is only a function of passband/
> stopband attenuations and transition band-width. However, in practical
> world would the transition bandwidth itself not a function of the
> filter cutoff frequency?
>
> For example, with 48K sampling frequency, if the filter cutoff is at
> 5000Hz, a transition BW of 500Hz probably can be considered
> acceptable. However, if the filter cutoff is at 100Hz, I would rather
> limit the transition BW till the next octave -- 200Hz, not till
> 100+500Hz. So given the same filter length (and hence passband/
> stopband attenuations and transition BW) a filter at 100Hz would
> perform worse compared to a filter at 5000Hz. If I want similar
> results at both frequencies, then lesser the cutoff frequency, greater
> should be the filter length.
>
> Does this appear right?

An easy way to look at this issue is I think to remember that the FIR
coefficients (which form the impulse response of the filter) are nothing
more than the Fourier transform of its frequency response. So the number of
taps is directly linked to the "resolution" of your filter in the frequency
domain. In your example you want to design a filter with a 5KHz cutoff and
500Hz transition. Let's assume that you select a sampling frequency around
40KHz (to have a reasonnable antialiasing filter). The filter processing
window is then from DC to 40/2=20KHz. As 20000/500=40 you need a filter with
significantly more than 40 taps, say around 100. I've not tried Rabiner's
formula but that should be close.

Friendly,
Robert Lacoste
www.alciom.com

On 28 Aug, 18:53, matcho_pla...@yahoo.com wrote:
> Hi all,
> I have a questions regarding FIR filter length. Usually, as per
> formulae from Kaiser or Hermann, it is only a function of passband/
> stopband attenuations and transition band-width. However, in practical
> world would the transition bandwidth itself not a function of the
> filter cutoff frequency?

No, provided we agree that "cutoff frequency" means "cutoff
frequency normalized with trespect to sampling frequency."

> For example, with 48K sampling frequency, if the filter cutoff is at
> 5000Hz, a transition BW of 500Hz probably can be considered
> acceptable. However, if the filter cutoff is at 100Hz, I would rather
> limit the transition BW till the next octave -- 200Hz, not till
> 100+500Hz. So given the same filter length (and hence passband/
> stopband attenuations and transition BW) a filter at 100Hz would
> perform worse compared to a filter at 5000Hz. If I want similar
> results at both frequencies, then lesser the cutoff frequency, greater
> should be the filter length.
>
> Does this appear right?

These are not differences in filter characteristics, they are
differences in specifications. Given a specific transition bandwidth,
the windowed FIR filters would be the same lengths regardless
of in what frequency range the cut-off is.

Whether any given transition bandwidth is actually useful,
is a completely different question alltogether.

Rune

On Aug 29, 2:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 28 Aug, 18:53, matcho_pla...@yahoo.com wrote:
>
> > Hi all,
> > I have a questions regarding FIR filter length. Usually, as per
> > formulae from Kaiser or Hermann, it is only a function of passband/
> > stopband attenuations and transition band-width. However, in practical
> > world would the transition bandwidth itself not a function of the
> > filter cutoff frequency?
>
> No, provided we agree that "cutoff frequency" means "cutoff
> frequency normalized with trespect to sampling frequency."
>
> > For example, with 48K sampling frequency, if the filter cutoff is at
> > 5000Hz, a transition BW of 500Hz probably can be considered
> > acceptable. However, if the filter cutoff is at 100Hz, I would rather
> > limit the transition BW till the next octave -- 200Hz, not till
> > 100+500Hz. So given the same filter length (and hence passband/
> > stopband attenuations and transition BW) a filter at 100Hz would
> > perform worse compared to a filter at 5000Hz. If I want similar
> > results at both frequencies, then lesser the cutoff frequency, greater
> > should be the filter length.
>
> > Does this appear right?
>
> These are not differences in filter characteristics, they are
> differences in specifications. Given a specific transition bandwidth,
> the windowed FIR filters would be the same lengths regardless
> of in what frequency range the cut-off is.
>
> Whether any given transition bandwidth is actually useful,
> is a completely different question alltogether.
>
> Rune

I agree. For a given transition BW, filter length is same irrespective
of the location of cutoff frequency. However, the lower the cutoff
frequency, the lower the transition bandwidth should also be for the
filter to be equally "useful" or able to reject frequencies outside
the passband.

Thanks a lot for all the responses.

Best regards,