MATLAB: Fft normalization and parseval

normalization and parseval

    h=complex(randi([-1 1],128,1),randi([-1 1],128,1));
    h=h/std(h); % no h is normalized to unit pow thus var(h)=1
    t=128*ifft(h);
    k=var(t);
    f=fft(t)/128
    g=var(f);
my problem is that k(power in time ) not = g(power in freq) also i have done normalizatoin so that parseval therom applies
any help please

Best Answer

also i have done normalizatoin so that parseval therom applies
No, you haven't, I'm afraid. For a length-N fft, the proper normalization is
   Y=fft(X)/sqrt(N);
   XX=sqrt(N)*ifft(Y);
For example,
>> X=rand(1,10);
>> Y=fft(X)/sqrt(10); XX= sqrt(10)*ifft(Y); 
>> norm(X), norm(Y), norm(XX)
ans =
      2.3117
ans =
      2.3117
ans =
      2.3117
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