Introduction to Fourier Analysis

Abstract

CONTINUOUS FOURIER ANALYSIS. Background. Fourier Series for Periodic Functions. The Fourier Integral. Fourier Transforms of Some Important Functions. The Method of Successive Differentiation. Frequency-Domain Analysis. Time-Domain Analysis. The Properties. The Sampling Theorems. DISCRETE FOURIER ANALYSIS. The Discrete Fourier Transform. Inside the Fast Fourier Transform. The Discrete Fourier Transform as an Estimator. The Errors in Fast Fourier Transform Estimation. The Four Kinds of Convolution. Emulating Dirac Deltas and Differentiation on the Fast Fourier Transform. THE USER'S MANUAL FOR THE ACCOMPANYING DISKS. Appendices. Answers to the Exercises. Index.