6.1 Introduction

In this chapter we consider the problem of compensating for some known frequency distortion over a given band. One form of distortion is an unwanted delay, and the resulting distortion is a phase variation that is linear with frequency. This particular case, of delay mismatch, was the subject of Chapter 5, and the method of correction, or equalization, used in Section 6.5 is basically the same as that in Section 5.3. However, we are also concerned with other forms of frequency distortion, and in this chapter the approach is more general, and amplitude variation over the band is included also. In order to do this, a new Fourier transform pair is introduced in Section 6.3, the ramp function, which is a linear slope across the band, and its transform, the snc ₁ function, which is the first derivative of the sinc function. In fact, a set of transform pairs is defined that are the integer powers of the frequency across the band (ramp ^r) and the derivatives of the corresponding order of the sinc function (snc _r). The sinc and rect functions are seen to be the first (or zeroth order) members of these sets. With these results, any amplitude variation, expressed as a polynomial function of frequency across the band of interest, has a Fourier transform that is a sum of snc _r functions. A simple example of amplitude equalization is given in Section 6.4.

The method of equalization outlined in Section 6.2...