TABLE OF CONTENTS The theoretical and practical discussions of the last chapter established the discrete Fourier transform (DFT) as a versatile, flexible and efficient analytical technique. It is central to the science of DSP, not just because it enables us to find out what frequencies are present in a signal, but also because many processing operations that can be conducted in the time domain may equally be conducted in the frequency domain, but with greater facility and speed. Nevertheless, because the DFT deals with discrete signals, there are certain stipulations and limitations governing its use of which we need to be aware; a solid understanding of these is vital for the correct interpretation of Fourier spectra, and for appropriate processing of signals using this method. In this chapter, we will take a detailed look at some of the more important properties of the DFT, the different ways of representing spectra, and finally some of the key processing operations that are frequently implemented using a Fourier-based approach.
A program called Fourier_Processor.exe demonstrates in a practical manner some of the properties associated with Fourier analysis and processing, and may be found on the CD that accompanies this book in the folder Applications for Chapter 7\ Fourier Processor\. This program allows you to import text files up to 32,768 values in length, compute Fourier transforms (up to the same length), display spectra in a variety of formats, and perform different key processing operations that we will discuss below. Because it uses...
