Digital Signal Processing with Examples in MATLAB, 2nd Edition

3

Correlation, Fourier Spectra, and the Sampling Theorem

3.1    Introduction

The word spectrum has several meanings. In signal processing, the spectrum of a signal is a particular type of mapping function. In the case of a waveform, the spectrum maps the signal from the time domain to the frequency domain, showing exactly how the signal content is distributed over frequency. In the case of an image, the spectrum maps the signal from the spatial domain of the image to a two-dimensional frequency domain. Sometimes, when we look at the signal in the frequency domain, the spectrum of a waveform or an image shows us things that we see less clearly or do not see at all in the time domain. It may, for example, bring out periodic components ...