Signals and Systems For Dummies

Chapter 14

The z-Transform for Discrete-Time Signals

In This Chapter

Traveling to the z-domain with the two-sided z-transform

Appreciating the ROC for left- and right-sided sequences

Using partial fraction expansion to return to the time domain

Checking out z-transform theorems and pairs

Visualizing how pole-zero geometry controls the frequency response

The z-transform (ZT) is a generalization of the discrete-time Fourier transform (DTFT) (covered in Chapter 11) for discrete-time signals, but the ZT applies to a broader class of signals than the DTFT. The ZT notation is also more user friendly than the DTFT. For example, linear constant coefficient (LCC) difference equations (see Chapter 7) can be solved by using just algebraic manipulation when the ZT is involved.

Here’s the deal: When a discrete-time signal is transformed with the ZT, it becomes a function of a complex variable; the DTFT creates a function of a real frequency variable only. The transformed signal is said to be ...