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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