TABLE OF CONTENTS All electrical signals can be described either as a function of time or of frequency. When we observe signals as a function of time they are called the time domain measurements. Sometimes, we observe the frequencies present in signals, in which case they are called the frequency domain measurements. The word spectrum refers to the frequency content of any signal.
When signals are periodic, time and frequency are simply related; namely, one is the inverse of the other. Then we can use the Fourier series to find the spectrum of the signal. For non-periodic signals, a Fourier transform is used to get the spectrum. However, performing a Fourier transformation involves integration over all time, i.e. from ? ? to + ?. Because this is not practically desired, we approximate the Fourier transform by a discrete Fourier transform (DFT), which is performed on a sampled version of the signal. The computational load for direct DFT, which is usually computed on a personal computer (PC), increases rapidly with the number of samples and sampling rate. As a way out of this problem, Cooley and Tukey invented the fast Fourier transform (FFT) algorithm in 1954. With FFT, the computational loads are significantly reduced.
In chapter 3 we discussed the basis of converting analogue signals to digital samples and vice versa for accurate digital processing of a time varying signal. Following fromt here, this chapter provides an overview of FFT techniques, as applied to dynamic signal...
