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Chapter 17

Ten Properties You Never Want to Forget

In This Chapter

Looking at significant properties you can’t live without as a signals and systems engineer

Seeing properties side by side between continuous and discrete signals and systems

A big wide world of properties is associated with signals and systems — plenty in the math alone! In this chapter, I present ten of my all-time favorite properties related to signals and systems work.

LTI System Stability

Linear time-invariant (LTI) systems are bounded-input bounded-output (BIBO) stable if the region of convergence (ROC) in the s- and z-planes includes the -axis and unit circle , respectively. The s-plane applies to continuous-time systems, and the z-plane applies to discrete-time systems. But here’s the easy part: For causal systems, the property is poles in the left-half s-plane and poles inside the unit circle of the z-plane.

Convolving Rectangles

The convolution of two identical rectangular-shaped pulses or sequences results in a triangle. The triangle peak is at the integral of the signal or sum of the sequence squared.

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