Digital Signal Processing

Abstract

In this chapter the concept of discrete-time signals and sampled-data systems implemented on digital hardware versus those of continuous-time signals driving analog systems and processes is introduced early on. The processes of signal sampling and analog signal reconstruction are then investigated, and the Nyquist sampling rate to avoid aliasing is explained by means of Fourier series analysis. Then the Z-transform is introduced as the tool of preference for analysis and synthesis of discrete-time linear, time-invariant systems defined by difference equations in the discrete time domain. A detailed account of the most important and practical continuous-time system mapping techniques to discrete-time ones is then presented. A brief account of digital filter structures and types is also given along with a presentation of the fast Fourier transform algorithm for the calculation of the discrete Fourier transform of discrete-time signals with finite duration admitting periodic expansion. The notions of waveform statistics as encountered in random signals and stochastic processes are then given in order to conclude with the effect on a random signal’s statistics due to its propagation through a linear, time-invariant system. Finally, concepts of optimal signal estimation and the Wiener filter are presented, leading to matched filter and zero-forcing equalizer parametric designs in the discrete-time domain.