Digital Video Processing for Engineers

12

Frequency Domain Representation

Chapter Outline

12.1 DFT and IDFT Equations

12.1.1 First DFT Example

12.1.2 Second DFT Example

12.1.3 Third DFT Example

12.1.4 Fourth DFT Example

12.2 Fast Fourier Transform

12.3 Discrete Cosine Transform

In this chapter we are going to examine the DFT (Discrete Fourier Transform) and its more popular cousin, the FFT (Fast Fourier Transform). The FFT is used in many applications, and we will see its uses in broadcast modulation and distribution systems. It also lays the basis for the DCT (Discrete Cosine Transform), commonly used in image compression, which is also covered.

This chapter has more mathematics than most of the others in this book. It requires some familiarity with basic trigonometry, complex numbers ...