There are methods to design digital IIR filters and there are other methods to design digital FIR filters.
Can anybody suggest a single design framework that can be used to derive either IIR or FIR filters?
I would also like the method to be flexible enough to design low-pass, band-pass, high-pass, filters and differentiators; all with a group delay that I can specify (i.e. not necessarily linear phase).
interesting q. Some thoughts ..( apologies for fishing in the dark )
1. Pole zero placement seems a likely candidate. Like Hough transform profiles in freq plots translate to single values of zeros and planes.
2. Maybe a basis in the freq domain can be obtained which translates to specific cluster of poles/ zeros . Then expressing profiles in freq domain as linear combination of these basis functions , perhaps a general design can be obtained..
Cheers
All the coefficients can be calculated by convolution of proper system design in the time domain.
The design techniques are classical and well understood. Go to the library. Study.
Some more thoughts:
1. H(z)=P(z)/Q(z).. both P and Q finite polynomials.
2. Q(z) can be expressed as infinite series e.g
1/(1-x)= 1 +x +x^2.... with condition IxI
The coefficients of filters can be calculated by MatLab.
The instruction is as follows,
[y,zf] = filter(b,a,X)
An example to determine a, and b in Butterworth filter,
Fs = 1000;
Fc = 50;
[B,A] = butter(1,2*pi*Fc/(Fs/2));
b0 = B(1);
b1 = B(2);
a1 = A(2);
So, the operation of convolution can be employed smoothly in time domain.
So I went to the library and did some study :) This is what I came up with ...
https://www.researchgate.net/publication/307545795
Conference Paper Optimal Design of Digital IIR and FIR Filters Using Complex ...
The paper is interesting but complex. Is it possible to publish an algorithmic approach so students could try to program iit or generate a module in Scilab. I had been posed a q by a student who wanted to know why discrete IIr filter is designed using analog filters. only, Text book answer is analog filters are well developed. Compliments. for unifying the approach.
Cheers
Yes, @Narasim, I'll post some worked examples. I wanted to do that in this paper, but I ran out of room.
Your student's question is a good one. I have been wondering the same thing for quite a while now. Digital IIR filter design doesn't need to start with an analog prototype and it doesn't need to involve numerical optimization procedures.
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