FOURIER TRANSFORMS

Fourier transform is one of the most important and often used integral transform. It is frequently applied for attaining the solutions to the problems of science and engineering such as image analysis, image filtering, image reconstruction, image compression, signal analyzing and circuit analysis. This transform is also effectively applied to initial and boundary value problems.

This book is to explore the basic concepts of Fourier transforms in a simple, systematic and easy-to-understand manner. The present book is divided into six chapters which cover all the important topics like Fourier transform, Fourier sine transform, Fourier cosine transform, finite Fourier sine transform, finite Fourier cosine transform and application of Fourier transforms.

Chapter 1 presents the introduction of Fourier transform. The definition of Fourier transform, inverse Fourier transform, properties of Fourier transform (Linearity; Damping; Shifting; Modulation; Derivative and Convolution) are presented in a brief manner in this chapter.

Chapter 2 deals with Fourier sine transform and inverse Fourier sine transform.

Chapter 3 discusses the Fourier cosine transform and inverse Fourier cosine transform.

Chapter 4 discusses the finite Fourier sine transform and inverse finite Fourier sine transform.

Chapter 5 discusses the finite Fourier cosine transform and inverse finite Fourier cosine transform.

Chapter 6 deals with the applications of Fourier transforms for solving partial differential equations.