| Author |
Message |
Richard Owlett
Guest
|
 Posted:
Sun Dec 11, 2005 1:16 am Post subject:
questions raised by reading and thinking with possibly missi |
|
|
I'm interested in speech recognition.
One of current problems seems to be requiring a "good" acoustic
environment. I have "gut feel" that appropriate filtering of input would
be useful.
That got me thinking of restrictions on filtering methods.
It also got me interested in DSP.
I start with a basic presupposition that however humans recognize speech
is, in some sense, the "best" way. That leads me to believe that any
filtering should be constant group delay -- ie linear phase.
I have an idea of what might be a useful frequency response - 4 or 5
'humps' corresponding to formant frequencies.
If implemented as a FIR filter can it be 'linear phase'.
Looking at a pdf discussing various windows, I think individual
frequency responses similar to shape of a "Blackman Window" would be
optimal. The individual pass band peaks would probably be at least a 1/2
octave apart.
what would be relative advantages of implementing:
1. by adding outputs of individual filters
2. a single filter with appropriate frequency response
Separate topic -- how many issues have I missed?
BTW -- Remember the number one rule of education: A paragraph in a book
doesn't give you a license to stop thinking.
(seen on WEB somewhere) |
|
| Back to top |
|
 |
Jerry Avins
Guest
|
| Posted:
Sun Dec 11, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Richard Owlett wrote:
...
| Quote: | I start with a basic presupposition that however humans recognize speech
is, in some sense, the "best" way. That leads me to believe that any
filtering should be constant group delay -- ie linear phase.
|
I don't see the connection between "human" and "constant group delay".
Is there an unexamined (or at least unexpressed) assumption involved?
| Quote: | I have an idea of what might be a useful frequency response - 4 or 5
'humps' corresponding to formant frequencies.
|
Formant frequencies vary among individuals, and we are very sensitive to
such variations. (I can distinguish my identical twin sisters by voice
or sneeze.)
| Quote: | If implemented as a FIR filter can it be 'linear phase'.
Looking at a pdf discussing various windows, I think individual
frequency responses similar to shape of a "Blackman Window" would be
optimal. The individual pass band peaks would probably be at least a 1/2
octave apart.
|
How would you measure the frequency response of a window? (I don't mean
to claim that you cant, provided other factors are specified.) Windows
are typically applied to time-domain data.
| Quote: | what would be relative advantages of implementing:
1. by adding outputs of individual filters
|
Easier to design?
| Quote: | 2. a single filter with appropriate frequency response
|
easier to program?
| Quote: | Separate topic -- how many issues have I missed?
|
I don't know. How many false assumptions have you made? At this stage,
spell out your assumptions, even if it seems tedious.
| Quote: | BTW -- Remember the number one rule of education: A paragraph in a book
doesn't give you a license to stop thinking.
(seen on WEB somewhere)
|
That's a good rule, but "the one rule"? Nah!
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
|
| Back to top |
|
|
Jerry Avins
Guest
|
| Posted:
Mon Dec 12, 2005 1:15 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Richard Owlett wrote:
| Quote: | Jerry Avins wrote:
Richard Owlett wrote:
...
I start with a basic presupposition that however humans recognize
speech is, in some sense, the "best" way. That leads me to believe
that any filtering should be constant group delay -- ie linear phase.
I don't see the connection between "human" and "constant group delay".
Is there an unexamined (or at least unexpressed) assumption involved?
Yes I was explicitly assuming the connection. Maybe "presuming" would be
a better word. But as it led to my question, we'll just take it as a
given whether or not it is an accurate description of reality.
I have an idea of what might be a useful frequency response - 4 or 5
'humps' corresponding to formant frequencies.
Formant frequencies vary among individuals, and we are very sensitive
to such variations. (I can distinguish my identical twin sisters by
voice or sneeze.)
Yes, and I was going to identify formant frequencies during training
mode. Doing much violence to standard nomenclature, I was thinking in
terms of "voice pass" and "interference stop" filters. The "why" and
"reasonableness" is *OT* for my question.
Please take as a given that I wish a passband filter with a particular
arbitrary lumpy shape which is also linear phase.
If implemented as a FIR filter can it be 'linear phase'.
Looking at a pdf discussing various windows, I think individual
frequency responses similar to shape of a "Blackman Window" would be
optimal. The individual pass band peaks would probably be at least a
1/2 octave apart.
How would you measure the frequency response of a window? (I don't
mean to claim that you cant, provided other factors are specified.)
Windows are typically applied to time-domain data.
Ahh, but that's why I said "the *SHAPE* of a 'Blackman Window' ".
I was looking at various windows and their transforms.
A DFT/IFT has no way of knowing that the numbers it feeds upon are in
time or frequency domain.
|
The the differences between the shapes of filters is subtle. If those
filters without steps at the ends, I find it difficult to distinguish a
Blackman from Nuttall, Blackman-Harris, von Hann, and others. What
distinguishing feature of Blackman attracts you?
| Quote: | what would be relative advantages of implementing:
1. by adding outputs of individual filters
Easier to design?
2. a single filter with appropriate frequency response
easier to program?
I'll try to rephrase in "domain neutral" terms.
-- Then again that will cause more problems than it's worth ;{
[--- perhaps very relevant side issue
If linear superposition applies in time/frequency domain, does
it survive FT to frequency/time domain followed by IFT back to
time/frequency domain?
---]
|
Yes
| Quote: | I'll restate my problem.
For arbitrary and unchangeable reasons I wish a filter defined in
frequency domain to have certain characteristics.
1. it *shall* be linear phase
2. its passband is of arbitrary shape
a. it can be treated as a whole
b. it can be seen as linear superposition of a few simple terms
So I repeat my basic question
What would be relative advantages of implementing:
1. by adding outputs of individual filters
|
Easier to design?
| Quote: | 2. a single filter with appropriate frequency response
|
Easier to program?
...
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
|
| Back to top |
|
|
Richard Owlett
Guest
|
| Posted:
Mon Dec 12, 2005 1:15 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Jerry Avins wrote:
| Quote: | Richard Owlett wrote:
...
I start with a basic presupposition that however humans recognize
speech is, in some sense, the "best" way. That leads me to believe
that any filtering should be constant group delay -- ie linear phase.
I don't see the connection between "human" and "constant group delay".
Is there an unexamined (or at least unexpressed) assumption involved?
|
Yes I was explicitly assuming the connection. Maybe "presuming" would be
a better word. But as it led to my question, we'll just take it as a
given whether or not it is an accurate description of reality.
| Quote: |
I have an idea of what might be a useful frequency response - 4 or 5
'humps' corresponding to formant frequencies.
Formant frequencies vary among individuals, and we are very sensitive to
such variations. (I can distinguish my identical twin sisters by voice
or sneeze.)
|
Yes, and I was going to identify formant frequencies during training
mode. Doing much violence to standard nomenclature, I was thinking in
terms of "voice pass" and "interference stop" filters. The "why" and
"reasonableness" is *OT* for my question.
Please take as a given that I wish a passband filter with a particular
arbitrary lumpy shape which is also linear phase.
| Quote: |
If implemented as a FIR filter can it be 'linear phase'.
Looking at a pdf discussing various windows, I think individual
frequency responses similar to shape of a "Blackman Window" would be
optimal. The individual pass band peaks would probably be at least a
1/2 octave apart.
How would you measure the frequency response of a window? (I don't mean
to claim that you cant, provided other factors are specified.) Windows
are typically applied to time-domain data.
|
Ahh, but that's why I said "the *SHAPE* of a 'Blackman Window' ".
I was looking at various windows and their transforms.
A DFT/IFT has no way of knowing that the numbers it feeds upon are in
time or frequency domain.
| Quote: |
what would be relative advantages of implementing:
1. by adding outputs of individual filters
Easier to design?
2. a single filter with appropriate frequency response
easier to program?
|
I'll try to rephrase in "domain neutral" terms.
-- Then again that will cause more problems than it's worth ;{
[--- perhaps very relevant side issue
If linear superposition applies in time/frequency domain, does
it survive FT to frequency/time domain followed by IFT back to
time/frequency domain?
---]
I'll restate my problem.
For arbitrary and unchangeable reasons I wish a filter defined in
frequency domain to have certain characteristics.
1. it *shall* be linear phase
2. its passband is of arbitrary shape
a. it can be treated as a whole
b. it can be seen as linear superposition of a few simple terms
So I repeat my basic question
What would be relative advantages of implementing:
1. by adding outputs of individual filters
2. a single filter with appropriate frequency response
| Quote: |
Separate topic -- how many issues have I missed?
I don't know. How many false assumptions have you made? At this stage,
spell out your assumptions, even if it seems tedious.
BTW -- Remember the number one rule of education: A paragraph in a
book doesn't give you a license to stop thinking.
(seen on WEB somewhere)
That's a good rule, but "the one rule"? Nah!
|
It only said "number one rule", it did not say "the *only* rule" ;) |
|
| Back to top |
|
|
Peter K.
Guest
|
| Posted:
Mon Dec 12, 2005 1:15 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Richard Owlett <rowlett@atlascomm.net> writes:
| Quote: | I'll restate my problem.
For arbitrary and unchangeable reasons I wish a filter defined in
frequency domain to have certain characteristics.
1. it *shall* be linear phase
2. its passband is of arbitrary shape
a. it can be treated as a whole
b. it can be seen as linear superposition of a few simple terms
So I repeat my basic question
What would be relative advantages of implementing:
1. by adding outputs of individual filters
|
This option might be nice if you're thinking along the lines of a
graphic equalizer: being able to arbitrarily change the gain (volume)
of a particular band of frequencies might be useful.
| Quote: | 2. a single filter with appropriate frequency response
|
This might be good if you know that the response doesn't have to
change much. Changing this sort of a filter on-the-fly, though, might
be problematic.
Ciao,
Peter K. |
|
| Back to top |
|
|
Randy Yates
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Richard Owlett <rowlett@atlascomm.net> writes:
| Quote: | Richard Owlett wrote:
...
That got me thinking ;
What are the *NECESSARY* conditions for a FIR filter of an arbitrary
shape in the frequency domain to be "linear phase".
One of the references I was reading stated that "a FIR filter would be
'linear phase' if its coefficients were symmetric about the middle
coefficient."
Is that a "sufficient" condition or a "necessary" condition?
What implication does it have for the passband response?
|
Hi Richard,
It is a sufficient condition. A trivial example of an FIR filter
that does not meet this condition but is still linear phase is
the FIR given by h[0] = 0, h[1] = 0, and h[2] = 1.
I've heard that a linear-phase filter has magnitude and phase
responses that are Hilbert transforms of each other, but I've
never been interested enough to investigate.
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% <yates@ieee.org> % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr |
|
| Back to top |
|
|
Richard Owlett
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Peter K. wrote:
| Quote: | Richard Owlett <rowlett@atlascomm.net> writes:
I'll restate my problem.
For arbitrary and unchangeable reasons I wish a filter defined in
frequency domain to have certain characteristics.
1. it *shall* be linear phase
2. its passband is of arbitrary shape
a. it can be treated as a whole
b. it can be seen as linear superposition of a few simple terms
So I repeat my basic question
What would be relative advantages of implementing:
1. by adding outputs of individual filters
This option might be nice if you're thinking along the lines of a
graphic equalizer: being able to arbitrarily change the gain (volume)
of a particular band of frequencies might be useful.
2. a single filter with appropriate frequency response
This might be good if you know that the response doesn't have to
change much. Changing this sort of a filter on-the-fly, though, might
be problematic.
Ciao,
Peter K.
|
It would be set once per "user". |
|
| Back to top |
|
|
Richard Owlett
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Jerry Avins wrote:
| Quote: | Richard Owlett wrote:
Jerry Avins wrote:
Richard Owlett wrote:
...
I start with a basic presupposition that however humans recognize
speech is, in some sense, the "best" way. That leads me to believe
that any filtering should be constant group delay -- ie linear phase.
I don't see the connection between "human" and "constant group
delay". Is there an unexamined (or at least unexpressed) assumption
involved?
Yes I was explicitly assuming the connection. Maybe "presuming" would
be a better word. But as it led to my question, we'll just take it as
a given whether or not it is an accurate description of reality.
I have an idea of what might be a useful frequency response - 4 or 5
'humps' corresponding to formant frequencies.
Formant frequencies vary among individuals, and we are very sensitive
to such variations. (I can distinguish my identical twin sisters by
voice or sneeze.)
Yes, and I was going to identify formant frequencies during training
mode. Doing much violence to standard nomenclature, I was thinking in
terms of "voice pass" and "interference stop" filters. The "why" and
"reasonableness" is *OT* for my question.
Please take as a given that I wish a passband filter with a particular
arbitrary lumpy shape which is also linear phase.
If implemented as a FIR filter can it be 'linear phase'.
Looking at a pdf discussing various windows, I think individual
frequency responses similar to shape of a "Blackman Window" would be
optimal. The individual pass band peaks would probably be at least a
1/2 octave apart.
How would you measure the frequency response of a window? (I don't
mean to claim that you cant, provided other factors are specified.)
Windows are typically applied to time-domain data.
Ahh, but that's why I said "the *SHAPE* of a 'Blackman Window' ".
I was looking at various windows and their transforms.
A DFT/IFT has no way of knowing that the numbers it feeds upon are in
time or frequency domain.
The the differences between the shapes of filters is subtle. If those
filters without steps at the ends, I find it difficult to distinguish a
Blackman from Nuttall, Blackman-Harris, von Hann, and others. What
distinguishing feature of Blackman attracts you?
|
I have a pdf of unknown title ( got saved as Windows.pdf ) written by
Craig Stuart Sapp <craig@ccrma.stanford.edu> 25 Feb 1997.
I has a collection of various windows and their transforms. The
particular Blackman window illustrated had a "nice" central lobe and all
the residual lobes were of "uniform" shape and at least 60 dB down.
*DARN YOU MR. AVINS*
You just made me read rather than just look at pretty pictures ;{
The plot of the particular Blackman-Harris window had max side lobes
another 20 dB down, but scale of drawing emphasized the side lobes near
the central one.
Transform of illustrated Hann window -- too much slop
Transform of illustrated Hann-Poisson window has a "pleasing shape" with
less "rejection" off central peak.
I've been "hit over head with 2x4" on another issue.
What a implications of all these being symmetric about some point.
Obviously if I'm going to have
"passband 1 of width a centered at freq b"
and
"passband 2 of width y centered at freq z"
what strange effects will asymmetry have?
| Quote: |
what would be relative advantages of implementing:
1. by adding outputs of individual filters
Easier to design?
2. a single filter with appropriate frequency response
easier to program?
I'll try to rephrase in "domain neutral" terms.
-- Then again that will cause more problems than it's worth ;{
[--- perhaps very relevant side issue
If linear superposition applies in time/frequency domain, does
it survive FT to frequency/time domain followed by IFT back to
time/frequency domain?
---]
Yes
I'll restate my problem.
For arbitrary and unchangeable reasons I wish a filter defined in
frequency domain to have certain characteristics.
1. it *shall* be linear phase
2. its passband is of arbitrary shape
a. it can be treated as a whole
b. it can be seen as linear superposition of a few simple terms
So I repeat my basic question
What would be relative advantages of implementing:
1. by adding outputs of individual filters
Easier to design?
2. a single filter with appropriate frequency response
Easier to program?
...
Jerry |
|
|
| Back to top |
|
|
Richard Owlett
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Richard Owlett wrote:
| Quote: | ...
That got me thinking ;
|
What are the *NECESSARY* conditions for a FIR filter of an arbitrary
shape in the frequency domain to be "linear phase".
One of the references I was reading stated that "a FIR filter would be
'linear phase' if its coefficients were symmetric about the middle
coefficient."
Is that a "sufficient" condition or a "necessary" condition?
What implication does it have for the passband response? |
|
| Back to top |
|
|
Ron N.
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Randy Yates wrote:
| Quote: | Randy Yates <yates@ieee.org> writes:
[...]
I've heard that a linear-phase filter has magnitude and phase
responses that are Hilbert transforms of each other, but I've
never been interested enough to investigate.
Sorry - correction!: Those are *minimum-phase* filters.
|
Minimum-phase FIR filters are interesting if speed of response
is more important than the phase linearity. For low pass filters,
minimum-phase filters would seem to me to be far more "natural"
than linear-phase filters, given that linear-phase low pass filters
have a "pre-ringing" response that sounds extremely unnatural
compared to any natural or analog filtering process. And
minimum-phase filters have the fastest mean response or
delay for a given pile of poles and zeros.
But the advantage of linear-phase filters for the OP is that,
given matched delays, they can be summed without worrying
about any phase cancellations of some frequency bands.
IMHO. YMMV.
--
rhn A.T nicholson d.O.t C-o-M |
|
| Back to top |
|
|
Randy Yates
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Randy Yates <yates@ieee.org> writes:
| Quote: | [...]
I've heard that a linear-phase filter has magnitude and phase
responses that are Hilbert transforms of each other, but I've
never been interested enough to investigate.
|
Sorry - correction!: Those are *minimum-phase* filters.
--
% Randy Yates % "Watching all the days go by...
%% Fuquay-Varina, NC % Who are you and who am I?"
%%% 919-577-9882 % 'Mission (A World Record)',
%%%% <yates@ieee.org> % *A New World Record*, ELO
http://home.earthlink.net/~yatescr |
|
| Back to top |
|
|
Ron N.
Guest
|
| Posted:
Tue Dec 13, 2005 1:16 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Randy Yates wrote:
| Quote: | Richard Owlett <rowlett@atlascomm.net> writes:
Richard Owlett wrote:
...
That got me thinking ;
What are the *NECESSARY* conditions for a FIR filter of an arbitrary
shape in the frequency domain to be "linear phase".
One of the references I was reading stated that "a FIR filter would be
'linear phase' if its coefficients were symmetric about the middle
coefficient."
Is that a "sufficient" condition or a "necessary" condition?
What implication does it have for the passband response?
....
It is a sufficient condition. A trivial example of an FIR filter
that does not meet this condition but is still linear phase is
the FIR given by h[0] = 0, h[1] = 0, and h[2] = 1.
|
That, to me, is just an obfuscation which can be remedied by
a more thorough definition of "middle coefficient", and the
addition/removal of up to an infinite number of zero terms.
IMHO. YMMV.
--
rhn A.T nicholson d.O.t C-o-M |
|
| Back to top |
|
|
Randy Yates
Guest
|
| Posted:
Tue Dec 13, 2005 7:20 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
"Ron N." <rhnlogic@yahoo.com> writes:
| Quote: | Randy Yates wrote:
Randy Yates <yates@ieee.org> writes:
[...]
I've heard that a linear-phase filter has magnitude and phase
responses that are Hilbert transforms of each other, but I've
never been interested enough to investigate.
Sorry - correction!: Those are *minimum-phase* filters.
Minimum-phase FIR filters are interesting if speed of response
is more important than the phase linearity. For low pass filters,
minimum-phase filters would seem to me to be far more "natural"
than linear-phase filters, given that linear-phase low pass filters
have a "pre-ringing" response that sounds extremely unnatural
compared to any natural or analog filtering process. And
minimum-phase filters have the fastest mean response or
delay for a given pile of poles and zeros.
|
Hey Ron, how do you know so much about minimum-phase filters? This
is still, at my ripe-old-age, one of the topics I have yet to broach
in my career.
Say, do you have an example of a linear-phase filter and corresponding
minimum-phase filter in which the linear-phase version exhibits the
"pre-ringing" phenomenom? I'd love to try this out for myself.
--
% Randy Yates % "Midnight, on the water...
%% Fuquay-Varina, NC % I saw... the ocean's daughter."
%%% 919-577-9882 % 'Can't Get It Out Of My Head'
%%%% <yates@ieee.org> % *El Dorado*, Electric Light Orchestra
http://home.earthlink.net/~yatescr |
|
| Back to top |
|
|
Ron N.
Guest
|
| Posted:
Tue Dec 13, 2005 9:07 am Post subject:
minimum phase filters (was Re: questions raised by reading a |
|
|
Randy Yates wrote:
| Quote: | "Ron N." <rhnlogic@yahoo.com> writes:
....
Minimum-phase FIR filters are interesting if speed of response
is more important than the phase linearity. For low pass filters,
minimum-phase filters would seem to me to be far more "natural"
than linear-phase filters, given that linear-phase low pass filters
have a "pre-ringing" response that sounds extremely unnatural
compared to any natural or analog filtering process. And
minimum-phase filters have the fastest mean response or
delay for a given pile of poles and zeros.
Hey Ron, how do you know so much about minimum-phase filters?
|
I don't. That I have anything at all to say about the topic falls
into the category of "random walk" continuing ed.
| Quote: | This is still, at my ripe-old-age, one of the topics I have yet to
broach in my career.
|
I was experimenting with cepstral methods for pitch recognition,
and found in my reading that a cepstrum calculation could also
be used to construct minimum phase FIR filters. There's a long
comp.dsp thread on the subject that I started somewhere around
mid-March of 2004.
| Quote: | Say, do you have an example of a linear-phase filter and corresponding
minimum-phase filter in which the linear-phase version exhibits the
"pre-ringing" phenomenom? I'd love to try this out for myself.
|
I don't have the c code handy, but I started with this description
found on the net:
| Quote: | wn = [ones(1,m); 2*ones((n+odd)/2-1,m) ; ones(1-rem(n,2),m);
zeros((n+od d)/2-1,m)];
y = real(ifft(exp(fft(wn.*real(ifft(log(abs(fft(x)))))))));
|
rewrote it, and fed it some very low pass (relative to the sample
rate) linear-phase FIR filters.
Minimum-phase FIR filters converted from symmetric windowed
Sincs can also be used for upsampling interpolation (and, if an
analog or physical filter was used for the original Nyquist
limiting process before sampling, a non-linear-phase reconstruction
might perhaps be closer to the original signal than a symmetric
windowed-Sinc reconstruction).
IMHO. YMMV.
--
rhn A.T nicholson d.O.t C-o-M |
|
| Back to top |
|
|
Guest
|
| Posted:
Tue Dec 13, 2005 9:15 am Post subject:
Re: questions raised by reading and thinking with possibly m |
|
|
Richard Owlett wrote:
| Quote: | Richard Owlett wrote:
...
That got me thinking ;
What are the *NECESSARY* conditions for a FIR filter of an arbitrary
shape in the frequency domain to be "linear phase".
One of the references I was reading stated that "a FIR filter would be
'linear phase' if its coefficients were symmetric about the middle
coefficient."
Is that a "sufficient" condition or a "necessary" condition?
|
We discussed this last June:
http://groups.google.com/group/comp.dsp/msg/9be6c8f2861d1d3a
| Quote: | What implication does it have for the passband response?
|
None that I could think of, apart from the linear phase.
Regards,
Andor |
|
| Back to top |
|
|
|
|
|
|
FAQ
Memberlist
Register
Profile
Log in to check your private messages
Log in