I have worked with it a bit in my time in physical layer test and measurement.
I’ll cover some quick basics then explain why chirp z is useful.
Ohm’s law: voltage = current * resistance. Resistance is considered a steady state value. Impedance is resistance across frequency. In the real world channels (cables, the air, etc.) do not have a flat impedance (the same resistance across all frequencies). Similarly, transmitters and receivers do not have flat resistance. If you try to send a signal through a channel that has too much insertion loss, then the receiver won’t be able to decode it. If the impedance of a transmitter/receiver is different than the channel there will be reflections that damage signal integrity (there are good/easy physical analogs to explain this, but I won’t. Think back to waves in physics class).
We can measure impedance over frequency directly using a vector network analyzer (VNA) or a time domain reflectometer (TDR). A VNA sweeps across frequencies and listens to the response. A TDR sends a pulse then waits for the response at a given delay. It sends many pulses and looks at many delays to build up an impedance over time plot. This impedance over time is very useful because it can show jumps in impedance at given electrical lengths. Like you can see impedance jump at 30 ns in where you expect to have the connector soldered to board, etc. However, TDRs compared to VNAs, are expensive, difficult to calibrate, and take data very slowly. So the industry has moved towards VNAs. However standards bodies (like the IEEE) are starting to appreciate the use of time domain impedance.
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.
To summarize: validating new hardware before mass production requires impedance measurement. Impedance measurement has two instrument options with large tradeoffs. Advancements in the chirp z algorithm reduce the penalties of one of those options.
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?
I’ll cover some quick basics then explain why chirp z is useful.
Ohm’s law: voltage = current * resistance. Resistance is considered a steady state value. Impedance is resistance across frequency. In the real world channels (cables, the air, etc.) do not have a flat impedance (the same resistance across all frequencies). Similarly, transmitters and receivers do not have flat resistance. If you try to send a signal through a channel that has too much insertion loss, then the receiver won’t be able to decode it. If the impedance of a transmitter/receiver is different than the channel there will be reflections that damage signal integrity (there are good/easy physical analogs to explain this, but I won’t. Think back to waves in physics class).
We can measure impedance over frequency directly using a vector network analyzer (VNA) or a time domain reflectometer (TDR). A VNA sweeps across frequencies and listens to the response. A TDR sends a pulse then waits for the response at a given delay. It sends many pulses and looks at many delays to build up an impedance over time plot. This impedance over time is very useful because it can show jumps in impedance at given electrical lengths. Like you can see impedance jump at 30 ns in where you expect to have the connector soldered to board, etc. However, TDRs compared to VNAs, are expensive, difficult to calibrate, and take data very slowly. So the industry has moved towards VNAs. However standards bodies (like the IEEE) are starting to appreciate the use of time domain impedance.
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.
To summarize: validating new hardware before mass production requires impedance measurement. Impedance measurement has two instrument options with large tradeoffs. Advancements in the chirp z algorithm reduce the penalties of one of those options.