Practical Signals Theory with MATLAB Applications

Linear Systems

LEARNING OBJECTIVES

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

• Describe the properties of a linear time invariant system
• Explain the difference between linear and nonlinear systems
• Describe the concept of response function
• Identify an ideal linear system
• Apply the convolution integral to find the output of a linear system
• Use MATLAB to define signals and to perform convolution operations
• Derive the output of a linear system given the response function
• Explain causality in terms of the impulse response of a linear system
• Apply the properties of a linear system to simplify system block diagrams

The mathematical modelling of systems allows the study of both signals and systems from a purely theoretical perspective. For an engineer, the understanding of the expected behavior of a system as it interacts with signals allows the efficient design and testing of systems both inside and outside the laboratory. In particular, linear systems represent an important class of systems based on the general properties of the system’s interaction with signals. Most of the systems described in this text will fall into the category of linear systems. For some nonlinear systems (such as transistor amplifiers), the operating conditions can often be constrained to satisfy the conditions of linearity. In other cases, a much more involved and nonintuitive analysis is required, ...