Handbook of Image and Video Processing, 2nd Edition

2.3

Basic Tools for Image Fourier Analysis

Alan C. Bovik,     The University of Texas at Austin

1 Introduction

2 Discrete-Space Sinusoids

3 Discrete-Space Fourier Transform

• Linearity of Discrete-Space Fourier Transform

• Inversion of Discrete-Space Fourier Transform

• Magnitude and Phase of Discrete-Space Fourier Transform

• Symmetry of Discrete-Space Fourier Transform

• Translation of Discrete-Space Fourier Transform

• Convolution and the Discrete-Space Fourier Transform

4 Two-Dimensional Discrete Fourier Transform

• Linearity and Invertibility of Discrete Fourier Transform

• Symmetry of Discrete Fourier Transform

• Periodicity of Discrete Fourier Transform

• Image Periodicity Implied by Discrete Fourier Transform

• Cyclic Convolution ...