Chapter 6 Part A Contents ●●● ●●● ●●● ●●● Part A:z-Transform z-Transform z-Transform Part B:Inverse z-Transform Part C:Transfer Function Part A:z-Transform 1.z-Transform 1.z-Transform The DTFT provides a frequency-domain In general,ZT can be thought of as a ◆z-Transform representation of discrete-time signals and LTI generalization of the DTFT.ZT is more Region of Convergence(ROC)of a discrete-time systems. complex than DTFT (both literally and Rational z-Transform Because of the convergence condition,in figuratively),but provides a great deal of many cases,the DTFT of a sequence may not insight into system design and behavior.For exist. discrete-time systems,ZT plays the similar role of Laplace-transform does in As a result,it is not possible to make use of such frequency-domain characterization in continuous-time systems.ZT characterizes these cases. signals or LTI systems in complex frequency domain.Chapter 6 z-Transform Part A z-Transform Contents Part A: z-Transform Part B: Inverse z-Transform Part C: Transfer Function 4 Part A: z-Transform z-Transform Region of Convergence (ROC) of a Region of Convergence (ROC) of a Rational z Rational z-Transform 5 1. z-Transform The DTFT provides a frequency-domain representation of discrete-time signals and LTI discrete-time systems. Because of the convergence condition, in Because of the convergence condition, in many cases, the DTFT of a sequence may not many cases, the DTFT of a sequence may not exist. As a result, it is not possible to make use of such frequency-domain characterization in these cases. 6 1. z-Transform In general, ZT can be thought of as a generalization of the DTFT. ZT is more complex than DTFT (both literally and figuratively), but provides a great deal of insight into system design and behavior. For discrete-time systems, ZT plays the similar role of Laplace Laplace-transform does in continuous-time systems. ZT characterizes signals or LTI systems in complex frequency complex frequency domain.