Practical Signals Theory with MATLAB Applications

The z-Transform

LEARNING OBJECTIVES

By the end of this chapter, the reader will be able to:

• Describe the difference between Fourier, Laplace, and z-transforms
• List the properties of the z-transform
• Identify the Fourier transform in the z-transform
• Explain the relationship between z-transform pairs
• Identify overall system behavior from a pole-zero diagram
• Apply the z-transform to analyze sampled systems
• Use MATLAB to analyze a system defined on z-transform parameters
• Apply the z-transform to frequency-domain filtering
• Describe the difference between FIR and IIR filters
• Use MATLAB to analyze the performance of FIR and IIR filters
• Design simple filters with specific properties using the z-transform

9.1 Introduction

In Chapter 8 the use of discrete time signals was described as an important consequence of using digital computers in signal processing. The analysis of sampled signals revealed a number of special properties of the Fourier transform with discrete time signals (DTFT). From these observations, it emerges that the application of digital signal processing (DSP) may benefit from a different transform that simplifies both the mathematics and the computational requirements by recognizing the special nature of discrete signals. The z-transform incorporates aspects of both the Fourier transform and the Laplace transform when dealing with discrete signals.

9.2 The z-Transform ...