9. Continuous-Time Signals and LTI Systems

We began this text with an introduction to continuous time signals and systems, and now we are going to return to that topic. While discrete-time systems have many virtues and we have emphasized them up this point, it is generally impossible to avoid some consideration of continuous-time signals and systems since most signals originate in continuous-time form.

In this chapter, we will begin with a review of our earlier discussion of continuous-time sinusoidal signals and then introduce several other basic signals that are important in the study of continuous-time systems. We will review the concepts of linearity and time-invariance and introduce the convolution representation of linear time-invariant systems. As part of our discussion, we will introduce the unit-impulse signal, which in the continuous-time case is a very strange, but very useful, mathematical concept. This concept is necessary to define the impulse response for LTI systems, which in turn leads to the concept of continuous-time convolution.

Homework

Labs - MATLAB

Lab 12: Two Convolution GUIs

This lab concentrates on the use of two MATLAB GUIs for convolution. dconvdemo: GUI for discrete-time convolution. This is exactly the same as the MATLAB functions conv() and firfilt() used to implement FIR filters. cconvdemo: GUI for continuous-time convolution. Each one of these demos illustrates an important point about the behavior of a linear, time-invariant (LTI) system. They also provide a convenient way to visualize the output of a LTI system.