# DSP Question: invfreqs.m

I generate some coefficents for a filter and can inspect the frequency response as following:

%%Orginal Data

N = 5000;

data = cumsum(randn(N,1));

t = 252;

a = 2 / (t+1);

b = repmat(1-a,1 ,N).^(1:N); %b are your filter coeff

b = b ./ sum(b);

a = 1;%%Plot the Filter on some example data

ma = filter(b, a, data);

figure;plot(data); hold all; plot(ma, 'r'); %%Plot the Response

figure;freqz(b,1);

[h,w] = freqz(b,1);

I now explain my problem. I am now in the situation where I have a frequency response (i.e. the vector “h”) and know nothing else.

I would like to estimate from this my original “b” (the filter coefficents) to allow me to estimate my variable “t”.

I thought I could use invfreqs.m (or invfreqz.m) to do this, but Im afraid I dont know how.

%%Find the impluse response

n = 10; % I choose a large number allowing a good approximation

m = 0; % I choose 0 here as I have 1 in my orignal filter ==> the output comes out as aNew = 1;

[bNew,aNew] = invfreqz(h,w,n,m);

%[bNew,aNew] = invfreqs(h,w,n,m);

sys = tf(bNew,aNew)%%Plot the filter coeffcients

x1 = [0: 1/(size(b,2) -1) : 1];

x2 = [0: 1/(size(bNew,2) -1) : 1];

figure;plot(x1,b); hold all; plot(x2,bNew, 'r');

When I inspect the final plot, I would expect to see the red line (bNew) as a good approximation to b. It is not. not even close.

Clearly I am doing something very wrong. Please could someone with experince of how this function works, explain my mistake.

many thanks!

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invfreqz.m has some odd rules re calling it.

%%Orginal Data

N = 5000;

data = cumsum(randn(N,1));

t = 252;

a = 2 / (t+1);

b = repmat(1-a,1 ,N).^(1:N);

b = b ./ sum(b);

a = 1;%%Plot the Filter on some example data

ma = filter(b, a, data);

figure;plot(data); hold all; plot(ma, 'r'); %%Plot the Response

figure;freqz(b,1, N);

[h,w] = freqz(b,1,N);%%Using dflit

% b = 1; a = -1; %Sanity Check. simple difference filter

% Hd = dfilt.df1([b a],1); % num/ denom == a/b

% fvtool(Hd);%%Find the impluse response

% If n>(N-1) then you get a random answer!

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