Chapter 6

Discrete-Time LTI Systems and the Convolution Sum

In This Chapter

arrow Getting familiar with the impulse response and the convolution sum

arrow Understanding the convolution sum and its properties

arrow Figuring out convolution sum problems

Chances are good that sometime within the last 24 hours you’ve interfaced with an electronic device that uses a discrete-time linear time-invariant (LTI) system. In fact, you’ve probably done so with more than one device! Surprised? Maybe not. The candidate devices I have in mind are popular ones, including digital music players, cellphones, HDTVs, and laptop computers.

Another name for a discrete-time LTI system is digital filter, and I cover the analysis and design of digital filters over multiple chapters in this book. The emphasis in this chapter is the time-domain view. (Check out Chapter 11 for details on the frequency domain and Chapter 14 for information on the z-domain view.)

The drill down in this chapter on the time-domain analysis, design, and behavior of discrete-time LTI systems leads to discrete-time convolution, or the convolution sum. The convolution sum is the mathematics of processing the input signal to the output of a digital filter. ...

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