generation of time series by given spetrum( ifft)

Hello!

i am trying to generate a time serie from a given kaimal spectrum.i am using ifft function but propably not in the correct way.I made a code but if i reverse by calculating the spectrum of the output time serie it give me different results. here is how i do it: =============================================================================== close all

clear all

%altitude 70meters

z=70;

%parameters of kaimal spectrum

U=20;

u=1;

%frequency

f=-0.5:0.001:0.5;

%n parameter of kaimal spectrum

n=f*z/U;

%definition of kaimal spectrum

%results of kaimal spectrum

S=u^2*(52.5*z/U)./((1+33*n).^(5/3));

%StD of S

StD_S=std(S);

%figure of the spectrum

figure

loglog(f,2*pi*S)

%generation of time series

N=1000;

a=randn(1,N/2);

b=randn(1,N/2);

X=StD_S*(a+1i*b);

A=conj(X);

B=[X A(end:-1:1)];

C=abs(ifft(B));

figure

plot(C)

======================================================================

 In generation of time serie i make a list of random complex number of N/2 length and multiply with the standard deviation of kaimail spectrum(i got it from theory that,so it sould be correct)
 The problem i think is in ifft.
Thanks anyway

Answer 1

[Dr. Seis]

In your case, you have:

Nyq = 0.5; % Nyquist frequency
df = 0.001; % frequency increment

Therefore, your array containing frequencies should be:

f = -Nyq : df : Nyq-df;

If you have amplitudes at each one of the frequencies described above (stored as B), you will then perform the IFFT by:

C = abs(ifft(ifftshift(B)));