Abstract
This chapter discusses the properties of linear time-invariant systems that are frequently encountered in analysis and design for practical applications. Linear time-invariant systems are characterized by the convolution sum. In this chapter, transfer functions and frequency response functions of linear time–invariant systems are described. First, it shows the frequency response of a system obtained by the input. Next, the chapter discusses the transfer function of a system represented by a linear constant coefficient difference equation. It presents a pole-zero plot of a transfer function on the z-plane, and the geometrical interpretation of the magnitude and phase response. Properties of linear system frequency responses are presented particularly in terms of the stability and causality. It describes the relationships between the real and imaginary parts of frequency response functions of real sequences. Finally, the chapter presents the decomposition of a transfer function into an all-pass and a minimum-phase system, and provides details regarding the basic idea of inverse filters.
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