Introduction

Abstract

Discrete-time/digital systems are originated from the continuous-time/analog world. It is the digital technology that transforms analog systems in continuous-time into the digital ones in discrete-time with the offer of unprecedented reliability and efficiency in large economic scale. This chapter begins with modeling of the inverted pendulum system using Lagrange mechanics. It covers state-space representation for multi-input/multioutput (MIMO) nonlinear dynamic systems and linearization of such state-space systems. Discretization of MIMO linear systems is studied based on step invariance transformation, and bilinear transformation with frequency warping. The phenomena of pathological sampling and non-minimum phase under high frequency sampling are described and analyzed.System models in discrete-time are also studied for digital communication systems. Digital data cannot be transmitted and received directly. They have to be modulated with continuous-time waveforms and converted to radio frequency (RF) signals prior to transmission and reception, leading to linear discrete-time systems. Continuous-time fading channels are introduced for wireless communications, and are derived under various assumptions. Discretization of the MIMO fading channels is carried via matching filter and ideal sampling. The discrete channel model is derived and analyzed. This chapter also includes a section on organization of the book.