Multidimensional Signal and Color Image Processing Using Lattices

5Continuous‐Domain Periodic Signals

5.1 Introduction

Chapters 2, 3 and 4 covered the cases of continuous‐domain aperiodic, discrete‐domain aperiodic, and discrete‐domain periodic signals and systems respectively. This chapter concludes the series with the case of continuous‐domain periodic signals. The results are very similar in flavor to the previous three cases, so a fairly brief rundown will be presented. This topic constitutes the multidimensional extension of one‐dimensional Fourier series representations of periodic signals. In the multidimensional case, periodicity is specified by a lattice . A periodic signal satisfies

(5.1)

Our only constraint here is that is a ‐dimensional lattice in . Again we use the to emphasize that a signal is periodic, and round parentheses to denote that ...