This paper traces methods of measuring frequency response and shows that Time Delay Spectrometry is a natural extension of such methods. A mathematical analysis shows how TDS measures the complex transfer function of a system, and calculated examples illustrate the effect of sweep rate and filter bandwidth. The demodulated chirp is usually stored in the memory of an associated display computer or analyzer, and post-processing of this data is feasible. If an undelayed demodulation chirp is used together with a fairly wideband output filter, then the output will represent the signals from a range of time delays. A software delay and output filter implementation is discussed which has a number of advantages, including multiple processing of data that needs to be captured only once, and application of digital output filters that show no spectral bias. An example of this technique is shown in unraveling the frequency responses of two loudspeakers whose simultaneously excited signals have very little difference in arrival time.
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