Effect of Nonlinear Group Delay on Signals

On 10 Sep, 05:30, "JM1970" <ra...@sbcglobal.net> wrote:
> >On 9 Sep, 06:38, "JM1970" <ra...@sbcglobal.net> wrote:
>
> >> Right after the original post, I decided, in the interest of time, to
> mod=
> >el
> >> the subject filter using bilinear transformation, but as pointed out
> in
> >> other posts, the accuracy of this approach is limited. =A0
>
> >Discrete-time (DT) versions of continuous-time (CT) prototypes
> >can only be approximations to the analog prototype, so the
> >'accuracy' has been compromised in the moment you decide
> >to use a DT version of the Chebychev filter.
>
> >Once you decide to make a DT Cheb filter, the obvious question
> >you will have to answer is "why don't you use the standard
> >method for designing the Cheb filter?"
>
> >If problems occur in your application, the fact that you
> >designed a standard filter by non-standard means will
> >undermine other people's confidence in you, and their
> >confidence in your competence and skills.
>
> >In summary:
>
> >- If you decide to use a Cheb filter, design it by the
> > &#4294967295;standard method.
> >- If you have any valid arguments why the standard Chebs
> > &#4294967295;are unsuitable for your application, don't use the Cheb.
>
> >And since the fact that you need such advice tells me
> >something about your skill level, I'll add another couple
> >of advices for free:
>
> >- Learn the basics of filters and filter design.
> >- There are some standard filtersing problems, where
> > &#4294967295;the standard Chebs are among the standard solutions.
>
> >There are very, very few standard applications where the
> >properties of the standard IIR filters render them useless.
> >So you should *really* know what you are talking about
> >before you start criticising the standard solutions to
> >the standard problems.
>
> >Rune
>
> Rune,
> I got all excited about the least squares approach due to its seeming
> flexibility in creating filters with arbitrary responses. &#4294967295;Your points are
> well taken. &#4294967295;

You should be aware that there are filter design methods around
(and have been, for a long time) that are fairly flexible. Again,
expect people to become curious or even sceptical of you if you
use non-standard methods to work the standard problems.

Doing so will indicate one of two:

1) You are an amateur who don't know the standard tools,
   in which case people are right in being sceptical of you.
   Which will do you no good.
2) You are way beyond the rest and have seen something
   in the problem others have not, that warrants the use
   of non-standard methods. In which case people are
   right in being sceptical of you, since most problems
   that appear to be standard in fact are standard. Which
   will do you no good.

So when you encounter a standard problem, stick to the
standard solutions.

Rune

>>JM1970 wrote:
>>> Hello, 
>>> I am trying to model the effect of group delay of an analog filter
>with
>>> complex transfer function H(f) on a phase modulated signal s(t), with
>a
>>> complex spectrum S(f). The analog filter I would like employ is a
>Chebyshev
>>> n=4, with 0.1dB ripple, but the exact filter is not important right
>now.  
>>> 
>>> In continuous time, the answer seems simple:  The filtered signal is
>just
>>> the inverse fourier transform of the product of S(f) and H(f).  
>>
>>How does that tell you the effect of (frequency dependent) group delay?
>>
>>> The concept for my discrete time model is the same, but I am unsure
if
>it
>>> volates any laws of DSP.  If I take N samples of s(t)at a rate fs,
>then
>>> perform an FFT of length Nfft=N,it is sampled in the frequency domain
>at
>>> intervals nfs/N, where n=0:N-1. If I sample the complex filter
>transfer
>>> function at these intervals, I get phasors H(f) that I can directly
>>> multiply the spectrum S(f)by to get the filtered spectrum SF(f),
where
>>> f=n*fs/N.  To get the filtered singal samples sf(nTs), perform the
IFFT
>of
>>> SF(f).  
>>
>>By modeling the impulse response, you get an impulse-invariant design. 
>>Google that to see what its disadvantages might be.
>>
>>> If there is a way to create a digital Chebyshev filter with the same
>>> magnigude and phase characteristics as an analog Chebyshev filter (or
>>> approximately), then it would seem possible to perform a fast
>convolution
>>> of the sampled signal, and the impulse response of the filter. Is
there
>a
>>> way to design a digital Chebyshev filter with phase equivalent to an
>analog
>>> counterpart?  I use linear-phase FIRs most of the time.
>>
>>Convolution is an FIR process. A Chebychev filter is an IIR structure. 
>>You would do well to design it in the usual way. Try the Java ap at 
>>http://www.dsptutor.freeuk.com/IIRFilterDesign/IIRFilterDesign.html
>>
>>Jerry
>>-- 
>>Engineering is the art of making what you want from things you can get.
>>�����������������������������������������������������������������������
>>Jerry,
>Thanks for the link to the coefficient calculator.  I will research
>inpulse invariant designs per your suggestion.  In answer to your
question,
>I figured the product of the two complex quantities H(f) and S(f) - the
>complex filter response and the complex signal response, respectively -
>would give the magnitude and phase response of the output Y(f).  If
>H(f)=A1(f)*exp(2pi*f*t+phi(f)) and s(f)=A2(f)*exp(2pi*f*t), then the
>product Y(f)=A1A2exp(2*pi*f*phi(f)), should be the filtered PSD, and if
the
>IFFT of this is computed, it should yield the filtered signal including
the
>effects of the group delay and attenuation characteristic of the filter
>described by H(f) (I think).  
>John M.
>I meant H(f)=A1(f)*exp(j*phi1(f)),s(f)=A2(f)*exp(j*phi2(f)) and 
Y(f)=A1(f)A2(f)*exp(phi1(f)+phi2(f)).