Fourier Transforms Using Mathematica

ISBN-13: 9781510638556

Joseph W. Goodman

Opis

The Fourier transform is a ubiquitous tool used in most areas of engineering and physical sciences. The purpose of this book is two-fold: (1) to introduce the reader to the properties of Fourier transforms and their uses, and (2) to introduce the reader to the program Mathematica (R) and demonstrate its use in Fourier analysis. Unlike many other introductory treatments of the Fourier transform, this treatment will focus from the start on both one-dimensional and two-dimensional transforms, the latter of which play an important role in optics and digital image processing, as well as in many other applications. It is hoped that by the time readers have completed this book, they will have a basic understanding of Fourier analysis and Mathematica.

Spis treści

• Introduction
• Some Useful 1D and 2D Functions
• Definition of the Continuous Fourier Transform
• Convolutions and Correlations
• Some Useful Properties of Fourier Transforms
• Fourier Transforms in Polar Coordinates
• Linear Systems and Fourier Transforms
• Sampling and Interpolation
• From Fourier Transforms to Fourier Series
• The Discrete Fourier Transforms
• The Fresnel Transform
• Fractional Fourier Transforms
• Other Transforms Related to the Fourier Transform
• Fourier Transforms and Digital Image Processing with Mathematica®
• Fourier Transforms and Mathematica® in Coherent Optical Systems