N = 1000; % Number of samples
df = 20; % Frequency increment (in Hertz)
Nyq = 10000; % Nyquist Frequency (in Hertz)
Two ways of determining Fs, but both should be same answer:
Fs = 2*Nyq; % Sampling frequency (20000 samples/sec)
Fs = N*df; % Sampling frequency (20000 samples/sec)
The real part of your frequency response is symmetrical (i.e., the real part of your FR is symmetrical about 0 frequency). The imaginary part of your frequency response is anti-symmetrical (i.e., the imaginary part of your FR is symmetrical about 0 frequency if you were to multiply one side by -1).
If you make sure you have frequency response amplitudes that corresponds to frequencies:
f = -Nyq : df : Nyq-df;
Then you can convert it into the timedomain using:
IR_data = ifft(ifftshift(FR_data));
Though there might be some scaling factor you will need to multiply the ifft result to (I think just multiply the result by Fs).
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EDIT 05/14/2012
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If you only have real, positive frequency data... then that's all you got. Imaginary parts are all zero, so that is fine... you have data with zero phase. You will still need to create a symmetrical dataset (i.e., "FR_data"). In order to create your "FR_data" dataset, you will take your current dataset, say "FR_positive_frequency_only" and do this:
FR_data = zeros(1,1000);
FR_data(2:501) = FR_positive_frequency_only;
FR_data(502:1000) = fliplr(FR_postive_frequency_only(1:end-1));
These amplitudes correspond to frequencies according to:
f_shift = ifftshift(f);
Your impulse response dataset is then just:
IR_data = ifft(FR_data); % No need to use ifftshift when constructing FR_data like above
Here the amplitude at 0 frequency (i.e., FR_data(1)) is just set to zero. Note: if your "FR_positive_frequency_only" dataset is a column matrix, then use flipud instead of fliplr.
