Xử lý tín hiệu số Z - transform Ngô Quốc Cường ngoquoccuong175@gmail.com Ngô Quốc Cường sites.google.com/a/hcmute.edu.vn/ngoquoccuong Z - transform • • • • Z- transform Properties of Z-transform Inversion of Z- transform Analysis of LTI systems in Z domain 4.1 Z - transform • Given a discrete-time signal x(n), its z-transform is defined as the following series: where z is a complex variable • Writing explicitly a few of the terms: • Z-transform is an infinite power series, it exists only for those values of z for this series converges • The region of convergence (ROC) of X(z) is the set of all values of z for which X(z) attains a finite value 4.1 Z - transform • Example: Determines the z-transform of the following finite duration signals 4.1 Z - transform • Solution 4.1 Z - transform • Example 4.1 Z - transform Recall that 4.1 Z - transform • Example • Solution 4.1 Z - transform • Example • We have (l = -n), • Using the formula (when A 0.5: • |z|[...]... 4.2 Properties of Z- transform • The ROC of z- k X (z) is the same as that of X (z) except for z= 0 if k>0 and z= ∞ if k |a| – The second... |z| < |b| 12 • Case 1 13 • Case 2 14 • Characteristics families of signals with their corresponding ROC 15 16 4.1 Z - transform • The z- transform of the impulse response h(n) is called the transfer function of a digital filter: • Determine the transfer function H (z) of the two causal filters 17 4.2 Properties of Z- transform 18 • Example 19 20 • Example 21 22 23 Exercise 24 25 4.2 Properties of Z- transform .. .Z - transform • • • • Z- transform Properties of Z- transform Inversion of Z- transform Analysis of LTI systems in Z domain 4.1 Z - transform • Given a discrete-time signal x(n), its z- transform. .. 4.1 Z - transform • Example 4.1 Z - transform Recall that 4.1 Z - transform • Example • Solution 4.1 Z - transform • Example • We have (l = -n), • Using the formula (when A