Evaluation of a Causal Time Domain Response from Bandlimited Frequency Domain Data

Abstract

Broadband measurements may be performed in either the time domain or the frequency domain. Time domain measurements are easier to perform since the waveforms of interest are all real However, one disadvantage is the limited dynamic range of available systems, whereas frequency domain measurement equipment benefits from large dynamic range. Also, it is difficult to recover the true time domain response from measurements made in a noisy environment. On the other hand, frequency domain measurements maybe carried out either over an entire range of frequencies or selectively over a band of frequencies, whichever is convenient and/or less susceptible to noise. From these measurements a time domain response can be extracted by an inverse Fourier transform. Since, bandlimited complex frequency domain data does not guarantee causality in the time domain, nor a real time domain response, measurements carried out in the frequency domain do not truly represent the transient response of the system.