Asked by Thomas Schäfer
on 11 Jun 2018

Hi I would like to perform an inverse fast Fourier transform on a measured set of data recorded with a network analyzer. The data I have is in the frequency domain and I am interested into transforming it to time domain. I have the frequency vector F and the corresponding complex magnitude vector V. I believe that the Matlab function IFFT is the function that I am looking for, but I cannot figure out how to set up the function call correctly. I would appreciate if someone would help me with this. Please let me know if I you need more info of my problem. I do not have access to the signal processing toolbox. Best regards Thomas

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## 4 Comments

## David Goodmanson (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405076-inverse-fast-fourier-transform-of-measured-rf-data#comment_577577

Hi Thomas,

the ifft requires equally spaced frequency points, so you have to be able to interpolate the data and to realistically extrapolate down to DC. Is that the case?

## Thomas Schäfer (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405076-inverse-fast-fourier-transform-of-measured-rf-data#comment_577639

Hi David Thank you for responding. As I mentioned the data is from measurement and is equally spaced in frequency. I have not made any interpolation or extrapolation. I have attached the data in a text file, first column is frequency (Hz), second is real part and third is imaginary. I expect a small contribution about 5ps (pico second) and larger around 130ps and 230ps. Best regards Thomas

## David Goodmanson (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405076-inverse-fast-fourier-transform-of-measured-rf-data#comment_578631

Hi Thomas,

I can't really comment on the picosecond times you are looking for, but the data does show a larger time delay tau on the order of 3 nsec, appearing as a multiplicative phase factor exp(2*pi*i*f*tau). The following code finds the delay and attempts to remove its effect.

I think it makes sense to rescale and use frequency in GHz so the times are in nanosec. The result is tau = 2.96 nsec which suggests about 0.8 m difference in cable length between the signal and reference channels (if all of the delay were due to that effect).

## Thomas Schäfer (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405076-inverse-fast-fourier-transform-of-measured-rf-data#comment_580022

Thank you for your replay. Yes, it is obvious after you point it out, that there is a longer transition line.

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