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Lecture Digital signal processing: Lecture 2 - Zheng-Hua Tan

In this lecture you will learn: System impulse response, linear constant-coefficient difference equations, fourier transforms and frequency response. Inviting you refer. | Digital Signal Processing Fall 2006 - E-Study - Lecture 2 Fourier transforms and frequency response Zheng-Hua Tan Department of Electronic Systems Aalborg University Denmark zt@kom.aau.dk 1 Digital Signal Processing II Zheng-Hua Tan 2006 Course at a glance MM7 MM3 MM9 MM10 2 Digital Signal Processing II Zheng-Hua Tan 2006 MM8 1 Part I System impulse response System impulse response Linear constant-coefficient difference equations Fourier transforms and frequency response 3 Digital Signal Processing II Zheng-Hua Tan 2006 AALBORG UNIVERSITY FIR systems reflected in the h n Ideal delay y n x n -nd -OT n X J h n 5 n - nd nd a positive integer. Forward difference d y n x n 1 - x n I 0 h n 0 n 1 - 0 n -1 1 Backward difference y n x n - x n -1 h n ố n - 5 n -1 0-p Finite-duration impulse response FIR system The impulse response has only a finite number of nonzero samples. 4 Digital Signal Processing II Zheng-Hua Tan 2006 AALBORG UNIVERSITY 2 IIR systems - reflected in the h n Accumulator y n Ỹx k k -J 1______ 5 h n x k u n 0 k -j Infinite-duration impulse response IIR system The impulse response is infinitive in duration. Stability S 2J -j h n J FIR systems always are stable if each of h n values is finite in magnitude. IIR systems can be stable e.g. h n anu n with a 1 S EJ a n 1 1- a J .A 5 Digital Signal Processing II Zheng-Hua Tan 2006 AALBORG UNIVERSITY Cascading systems Causality h n 0 n 0 Ideal delay h n ỗ n - nd x n Forward difference One - sameple delay h n ổ n 1 -ổ n h n ổ n -1 y n x n Backward difference h n 5 n -3 n -1 y n Any noncausal FIR system can be made cause by cascading it with a sufficiently long delay 6 Digital Signal Processing II Zheng-Hua Tan 2006