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Guest

Posted: Tue Dec 13, 2005 3:21 pm Post subject: Re: questions raised by reading and thinking with possibly m

Ron N. wrote:
....

Quote:

Minimum-phase FIR filters are interesting if speed of response
is more important than the phase linearity.

Also, if number of coefficients is important - a given magnitude
response can usually be met with less coefficients if the
phase-linearity condition is dropped.

Quote:

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.

Perhaps that is the reason why digital audio sounds so extremely
unnatural - it's them damn linear-phase reconstruction filters!

Regards,
Andor

Randy Yates
Guest

Posted: Tue Dec 13, 2005 5:16 pm Post subject: Re: questions raised by reading and thinking with possibly m

abariska@student.ethz.ch writes:

Quote:

Richard Owlett wrote:
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

Consider the filter coefficients determined as

function y = test(x)
%function y = test(x)
n = [-25 : 25];
Fs = 1;
Ts = 1/Fs;
t = n*Ts;
plot(sinc(t+1/7));

These are neither symmetric nor antisymmetric in the sense you defined,
and yet this is a linear phase filter, is it not?
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

Guest

Posted: Tue Dec 13, 2005 5:16 pm Post subject: Re: questions raised by reading and thinking with possibly m

Randy Yates wrote:

Quote:

abariska@student.ethz.ch writes:

Richard Owlett wrote:
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

Consider the filter coefficients determined as

function y = test(x)
%function y = test(x)
n = [-25 : 25];
Fs = 1;
Ts = 1/Fs;
t = n*Ts;
plot(sinc(t+1/7));

These are neither symmetric nor antisymmetric in the sense you defined,
and yet this is a linear phase filter, is it not?

No, it's not.

Regards,
Andor

Jerry Avins
Guest

Posted: Tue Dec 13, 2005 5:16 pm Post subject: Re: questions raised by reading and thinking with possibly m

Richard Owlett wrote:

Quote:

Jerry Avins wrote:

...

Quote:

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.

Those plots are not the shapes of the windows. Rather, they are the
shapes of the frequency responses obtained by applying the windows to a
filter, not at all what you wrote. Better shapes than any of them (but
not by much) are filters optimized by Parks-McClellan and such. Look up
"windowed sinc".

Quote:

*DARN YOU MR. AVINS*
You just made me read rather than just look at pretty pictures ;{

:-)

Quote:

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?

Try it and see. Won't ScopeDSP do it for you?

...

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

Jerry Avins
Guest

Posted: Tue Dec 13, 2005 5:16 pm 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."

Not very well put. With an even number of coefficients, there is no
middle one.

Quote:

Is that a "sufficient" condition or a "necessary" condition?
What implication does it have for the passband response?

A filter's phase response is linear *if and only if* it is symmetric or
antisymmetric about its middle. Note: Both [1 1] and [1 0 1] are
symmetric. Both [1 -1] and [1 0 -1] are antisymmetric. Exception:
adding zeros to one end of an otherwise symmetric or antisymmetric
filter doesn't impair its phase linearity.

Jerry

P.S. Most frequency-altering processes in nature affect phase.
Electronic means to restore a flat response without affecting phase
don't usually sound as good as a more complete correction.
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Peter K.
Guest

Posted: Tue Dec 13, 2005 5:16 pm Post subject: Re: questions raised by reading and thinking with possibly m

Randy Yates wrote:

Quote:

I'm with Andor:

Quote:

X = grpdelay(sinc(t+1/7),1,20);
X

X =

24.7190
24.8790
24.9947
24.7873
24.7215
24.9915
24.9908
24.5986
24.7294
25.6582
32.6615
25.6582
24.7294
24.5986
24.9908
24.9915
24.7215
24.7873
24.9947
24.8790

Compare that with:

Quote:

X2 = grpdelay(sinc(t),1,20);
X2

X2 =

25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000
25.0000

Ciao,

Peter K.

Jerry Avins
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Randy Yates wrote:

Quote:

"Peter K." <p.kootsookos@iolfree.ie> writes:

[...]
I'm with Andor:

X = grpdelay(sinc(t+1/7),1,20);
X

X =

24.7190
24.8790
[...]

Those ripples are apparently from truncation. I haven't
proved it, but the longer you extend the sequence, the
smaller they become.

As I stated to Andor, I think

b[n] = sinc(n + 1/7)

is linear phase, and doesn't match the symmetric/antisymmetric
requirement.

Think about it: If you start with a linear phase impulse response,
then delay it by a fractional sample amount, it's still linear phase,
but it ain't necessarily symmetric anymore.

The symmetry condition is sufficient, not necessary.

I think I stated earlier, in an oblique way tailored to Richard, that
pure delay added to a linear-phase transfer function won't impair the
phase linearity. b[n] = sinc(n + 1/7 is only pure delay when n ranges
from negative to positive infinity. We didn't start this discussion soon
enough and I won't be around to see it through. :-)

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

Peter K.
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Randy Yates <yates@ieee.org> writes:

Quote:

Certainly! The Clements and Pease paper (see
http://0xdc.com/CLPIIR.html for an example) showed that there exist
causal, IIR, linear phase impulse responses... they're just not
realizable using rational transfer functions.

Ciao,

Peter K.

Richard Owlett
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Jerry Avins wrote:

Quote:

Richard Owlett wrote:

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."

Not very well put. With an even number of coefficients, there is no
middle one.

The reference I was reading seemed to treat that as a degenerate case.

Quote:

Is that a "sufficient" condition or a "necessary" condition?
What implication does it have for the passband response?

A filter's phase response is linear *if and only if* it is symmetric or
antisymmetric about its middle. Note: Both [1 1] and [1 0 1] are
symmetric. Both [1 -1] and [1 0 -1] are antisymmetric. Exception:
adding zeros to one end of an otherwise symmetric or antisymmetric
filter doesn't impair its phase linearity.

Picking numbers *AT RANDOM*
Are you saying that a "low pass" filter with an overall passband of 10
kHz with "peaks" at 2 kHz, 3.14 kHz, and 7.9631 kHz with relative
amplitudes of 1, 2.91234, and 1.167 *could not* be linear phase?

Quote:

Jerry

P.S. Most frequency-altering processes in nature affect phase.
Electronic means to restore a flat response without affecting phase
don't usually sound as good as a more complete correction.

Huh. I'm not natural (so to speak ;)

Randy Yates
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

abariska@student.ethz.ch writes:

Quote:

Randy Yates wrote:
abariska@student.ethz.ch writes:

Richard Owlett wrote:
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

Consider the filter coefficients determined as

function y = test(x)
%function y = test(x)
n = [-25 : 25];
Fs = 1;
Ts = 1/Fs;
t = n*Ts;
plot(sinc(t+1/7));

These are neither symmetric nor antisymmetric in the sense you defined,
and yet this is a linear phase filter, is it not?

No, it's not.

True, but this is:

b[n] = sinc(n + 1/7)

The truncation was unintended - just to get a plot in Matlab.
--
% Randy Yates % "My Shangri-la has gone away, fading like
%% Fuquay-Varina, NC % the Beatles on 'Hey Jude'"
%%% 919-577-9882 %
%%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Randy Yates
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

"Peter K." <p.kootsookos@iolfree.ie> writes:

Quote:

[...]
I'm with Andor:

X = grpdelay(sinc(t+1/7),1,20);
X

X =

24.7190
24.8790
[...]

Those ripples are apparently from truncation. I haven't
proved it, but the longer you extend the sequence, the
smaller they become.

As I stated to Andor, I think

b[n] = sinc(n + 1/7)

is linear phase, and doesn't match the symmetric/antisymmetric
requirement.

Think about it: If you start with a linear phase impulse response,
then delay it by a fractional sample amount, it's still linear phase,
but it ain't necessarily symmetric anymore.

The symmetry condition is sufficient, not necessary.
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

Ron N.
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Randy Yates wrote:

Quote:

abariska@student.ethz.ch writes:

Randy Yates wrote:
abariska@student.ethz.ch writes:

Richard Owlett wrote:
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

Consider the filter coefficients determined as

function y = test(x)
%function y = test(x)
n = [-25 : 25];
Fs = 1;
Ts = 1/Fs;
t = n*Ts;
plot(sinc(t+1/7));

These are neither symmetric nor antisymmetric in the sense you defined,
and yet this is a linear phase filter, is it not?

No, it's not.

True, but this is:

b[n] = sinc(n + 1/7)

This is a symmetric filter plus a fractional tap delay, or vice
versa. Given a perfectly bandlimited filter function, no truncation,
and infinite precision, the fractional delay should be linear in
phase delay. Practically, it's a little harder to analyze than
a set of symmetric tap coefficients, which are linear phase
even with lots of (symmetric) truncation, and (symmetric)
quantization.

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

Richard Owlett
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Randy Yates wrote:

Quote:

abariska@student.ethz.ch writes:

Richard Owlett wrote:

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

Consider the filter coefficients determined as

function y = test(x)
%function y = test(x)
n = [-25 : 25];
Fs = 1;
Ts = 1/Fs;
t = n*Ts;
plot(sinc(t+1/7));

These are neither symmetric nor antisymmetric in the sense you defined,
and yet this is a linear phase filter, is it not?

je ne comprend pas ;]

Can you give me code understood by Scilab so I can know what point you
wish to make ;[

Vladimir Vassilevsky
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Jerry Avins wrote:

Quote:

Don't look at the transient response and linear phase will sound just as
good as the minimal phase :) We are entering the area of the holy wars
of the blunt-pointed vs sharp pointed. From my experience the only
observable difference results from the implementation issues like
overflows, loss of accuracy, group delay or frequency response mismatch
and such.

BTW, what do you think about Bessel filters, which are the minimum phase
approximations of the linear phase?

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Jerry Avins
Guest

Posted: Wed Dec 14, 2005 1:16 am Post subject: Re: questions raised by reading and thinking with possibly m

Richard Owlett wrote:

...

Quote:

No. You seem to still be confusing a filter's (or a window's) frequency
response with FIR coefficients.

Quote:

P.S. Most frequency-altering processes in nature affect phase.
Electronic means to restore a flat response without affecting phase
don't usually sound as good as a more complete correction.

Huh. I'm not natural (so to speak ;)

A linear-phase phono equalizer completely louses up the transient
response. A "perfect" linear-phase speaker crossover often sounds much
worse that the minimum-phase analog approximation that it replaced.

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

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