Now to why chirp z is useful. You can reversibly convert from the time domain to the frequency domain using a fourier transform. Great. You just have to assume that your signal repeats for all time. Hmm. Zero pad and don’t worry about it. What do we not get from this assumption though? Low frequency information. So let’s start with a frequency domain data set (a la VNA) and convert to the time domain. Well that missing low frequency information is very important. You can extrapolate the missing values. The error in the extrapolation will shift your entire impedance profile by huge amounts. In comes chirp z. It is able to handle the missing spectrum much better than the fourier transform.
So, it seems likely that you're right about the CZT being used in time-domain netowrk analysis, since I've seen documentation indicating that it was used for that purpose as far back as the HP 8510.[1] But I still don't grok why, and Rytting's brief explanation on page 13 of that document makes no sense whatsoever.
From a practical perspective, the chirp-Z transform just lets us use arbitrary start/end frequencies rather than the entire DC-Nyquist range that traditional FFTs encompass, correct? If I'm emulating lowpass TDR with a VNA, I'll have to extrapolate the DC response, as you point out... but what specifically makes the CZT better suited to this extrapolation process?
So, it seems likely that you're right about the CZT being used in time-domain netowrk analysis, since I've seen documentation indicating that it was used for that purpose as far back as the HP 8510.[1] But I still don't grok why, and Rytting's brief explanation on page 13 of that document makes no sense whatsoever.
From a practical perspective, the chirp-Z transform just lets us use arbitrary start/end frequencies rather than the entire DC-Nyquist range that traditional FFTs encompass, correct? If I'm emulating lowpass TDR with a VNA, I'll have to extrapolate the DC response, as you point out... but what specifically makes the CZT better suited to this extrapolation process?
[1]: http://hparchive.com/seminar_notes/a-137.pdf