tailieunhanh - Bài giảng Xử lý tín hiệu số: Chương 5 - TS. Hà Hoàng Kha

Bài giảng "Xử lý tín hiệu số - Chapter 5: z-Transform" gồm có những nội dung chính sau: z-Transform, properties of the z-transform, causality and stability, inverse z-transform, and other contents. Mời các bạn cùng tham khảo. | Chapter p 5 z-Transform Ha Hoang Kha to edit Master subtitle style Ho Chi Minh City University of Technology @ Email hhkha@ https tailieudientucntt The z-transform is a tool for analysis design and implementation of discrete time signals and LTI systems. discrete-time systems Convolution in time-domain multiplication in the z-domain Ha H. Kha 2 z-Transforms https tailieudientucntt Content 1 z-transform 1. t f 2. Properties of the z-transform 3. Causality and Stability 4. Inverse z-transform Ha H. Kha 3 Discrete-Time Systems https tailieudientucntt 1. The z-transform The z-transform of a discrete-time signal x n is defined as the power series X z x n n z n x 2 z 2 x 1 z x 0 x 1 z 1 x 2 z 2 The region of convergence ROC of X z is the set of all values of z for f which hi h X X z attains i a finite fi i value. l ROC z C X z x n z n n The z-transform of impulse response h n is called the transform function of the filter H z h n n z n Ha H. Kha 4 z-Transforms https tailieudientucntt Example Determine the z-transform of the following finite-duration signals a x1 n 1 2 5 7 0 1 b x2 n x1 n-2 c x3 n x1 n 2 d x4 n δ n e x5 n δ n-k n δ n k k gt 0 f x6 n δ n k k gt 0 Ha H. Kha 5 z-Transforms https tailieudientucntt Example Determine the z-transform of the signal 0 5 nu n a x n b x n - nu -n-1 Ha H. Kha 6 z-Transforms https tailieudientucntt z-transform and ROC It is possible for two different signal x n to have the same z- transform. Such signals g can be distinguished g in the z-domain byy their region of convergence. z-transforms and their ROCs ROC of a causal signal is the ROC of an anticausal signal exterior t i off a circle. i l is the interior of a circle. circle Ha H. Kha 7 z-Transforms https tailieudientucntt Example Determine the z-transform of