Advanced Engineering Mathematics, 7th Edition

15.5 Finite Fourier Transforms

INTRODUCTION

The two integral transform pairs considered in this section are a bit different from those considered in Section 15.4. The finite Fourier cosine and sine transforms are based not on the Fourier integral, but rather on the Fourier cosine and sine series discussed in Section 12.3. The transform of a function f is an integral, whereas the inverse transform is a Fourier series.

Finite Transforms

We begin with the definitions of the finite Fourier cosine and sine transforms. Before reading Definition 15.5.1, we suggest that you review Definition 12.3.1. Let f be a function defined on the interval