# use IFFT (matlab) for transforming frequency domain to time domain

Question asked by meta5718 on Mar 28, 2014
Latest reply on Mar 20, 2017 by haj

I am doing some scattering measurement (RCS) in X band using VNA and a pair of horns. Some references suggest that using time gating can reduce noise. It was also mentioned that this can be achieved by using software (Matlab) to process the measured data (S21). Since our VNA does not have the time domain option, I am looking into this software method.

After reading the application note (http://cp.literature.agilent.com/litweb/pdf/5989-5723EN.pdf) and a few previous posts, my initial attempt is to use IFFT of Matlab on a finite bandwidth, measured S21 (say 8-14 GHz), which is complex. My understanding is that this is corresponding to the bandpass mode of VNA. And I am only interested in the magnitude of the time domain data.

In previous posts "S21 time domain response ", "https://community.keysight.com/message/4826#comment-4826 ", there are some discussions on the bandpass mode.

_"In bandpass mode, the IFT is not analytically correct, for some non-obvious reasons. One key point is that the band pass transform does not assume a hermitian response, but rather, computes the response as though the data taken is single sided, with the "negative" frequency response being zero, rather than identical to the positive with opposite sign. The Low Pass mode makes the assumption that the negative frequency response is of the same magnitude and opposite phase, so in effect, creates data at negative frequencies. Doing this in low pass mode assures a pure real transform. In the band pass transform, the response is not pure real, but in fact must always be complex._

_The band pass response is computed by frequency shifting the data such that the center point is at DC, computing the IFT (complex form, as the data is not hermitian about the center point except in special cases), then applying the Fourier shift theory in the time domain to multiply the result by e^(jwt) where w is the center frequency of the "pre-shifted" data. Thus, you will see a cosine (on the real) and a sine (on the imaginary) data imposed on the low pass response (sometime this is called the modulation theorem as well)._

The modulation by e^(jwt) makes sense. Now since only the magnitude of S21 in time domain is concerned, does it mean that this factor can be dropped? In other word, simply applying the inverse Fourier transform will generate the time domain data for me?

One related question is that where is the t0 (starting time)? Does the transformed time domain start at t=0s? I guess in theory the time domain data is infinite and periodic. But is it possible to locate the t=0, or reference time? Apparently this can help to identify the scattering signal from the object since the distance between the transmitter is known.

Thanks!