Practical Signals Theory with MATLAB Applications

Introduction to Signals and Systems

In this chapter, basic definitions essential to the study of signals and systems are introduced. While some of these concepts will undoubtedly seem familiar, they are presented here in the context of electrical engineering applications and in terms of specific properties that will prove important in signals analysis. The mathematical operations of shifting, scaling, and multiplication are related to signal delays, time compression, and amplification. Emphasis is placed on employ ing linear combinations of simple signal types to aid the study of new and interesting functions. A variety of graphical and arithmetic examples are presented. Features of MATLAB used to manipulate and to plot various signals are highlighted.

LEARNING OBJECTIVES

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

• Write the definitions of a signal and a system
• Define continuous-time and discrete-time signals
• Explain the mathematical basis of shifting, scaling, and multiplication
• Describe the shifting, scaling, and multiplication operations graphically
• Identify a linear combination of signals
• Describe basic signals in standard form: unit rectangle, unit step, impulse, comb, sinusoid
• Create and sketch new signals as linear combinations of the basic signals
• Identify variations of the basic signals by component
• Apply mathematical operations to describe new signals in ...