Chapter 5 - Linear Systems in the Frequency Domain: The Transfer Function

Abstract

Publisher Summary This chapter presents a discusion of linear systems in a frequency domain. Linear systems can be represented by differential equations and transfer functions that are combinations of four basic elements. If signals are restricted to steady-state sinusoids, then phasor techniques can be used to represent these elements by algebraic equations that are functions of only frequency. Phasor techniques represent steady-state sinusoids as a single complex number. With this representation, the calculus operation of differentiation can be implemented in algebra simply as multiplication by jω, where j = √(−1) ω is frequency in radians. If all the elements in a system can be represented by algebraic operations, they can be combined into a single equation termed the transfer function. The transfer function relates the output of a system to the input through a single equation. The transfer function can only deal with signals that are sinusoidal or can be decomposed into sinusoids. The transfer function not only offers a succinct representation of the system, it also gives a direct link to the frequency spectrum of the system. The concepts of analog and system representations of linear processes are explained in the chapter. It explains linearity, time invariance, causality, and superposition. The response of system elements to sinusoidal inputs is also discussed in the chapter.