Multidimensional Signal and Color Image Processing Using Lattices

4Discrete‐Domain Periodic Signals

4.1 Introduction

This chapter is concerned with discrete‐domain signals, defined on a lattice , that are periodic. This means that there is another lattice that is a sublattice of that defines the periodicity. We can develop a complete theory for signal spaces of periodic signals, and linear shift‐invariant systems acting on elements of these signal spaces. Once again, the Fourier transform is a key tool for the analysis of such signals and systems. The resulting Fourier transform in this case is the multidimensional extension of the well‐known discrete Fourier transform (DFT), and also has available the same family of fast computation algorithms, namely the fast Fourier transform (FFT).

4.2 Periodic Signals

Let be a lattice in dimensions and a ‐dimensional ...