tailieunhanh - Lecture Digital signal processing: Lecture 4 - Zheng-Hua Tan

Lecture Digital signal processing - Lecture 4 present sampling and reconstruction. The main contents of this chapter include all of the following: Periodic sampling, frequency domain representation, reconstruction, changing the sampling rate using discretetime processing. | Digital Signal Processing Fall 2006 Lecture 4 Sampling and reconstruction Zheng-Hua Tan Department of Electronic Systems Aalborg University Denmark zt@ 1 Digital Signal Processing IV Zheng-Hua Tan 2006 Course at a glance MM3 MM9 MM10 MM7 MM8 ___________ 1 Mt 2 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY 1 Part I Periodic sampling Periodic sampling Frequency domain representation Reconstruction Changing the sampling rate using discretetime processing 3 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY Periodic sampling From continuous-time Xc ft to discrete-time x n x n xc nT -TO n x Sampling period T Sampling frequency fs 1 T Qs 2n T C D _____ jr n xcinTị Block diagram 1 representation of an ideal continuous-to-discrete-time C D converter. 4 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY 2 Two stages In practice I inversion from impulse rain lo discrete-time c The output sequence for the two different sampling rates Mathematically Impulse train modulator Conversion of the impulse train to a sequence co s t Y t - nT n -w x t xc t s t co Xc t ZS t - nT n -w Ỹ xc nT S t - nT n -w x n xc nT - x n x w z c- J 1 xc t J xc r 8 t -T d T 5 Digital Signal Processing r Figure Sampling with a periodic impulse tram followed by conversion to a discrete-time sequence a Overall system b Xj 0 for two sampling rates Periodic sampling Tow-stage representation Strictly a mathematical representation that is convenient for gaining insight into sampling in both the time and frequency domains. Physical implementation is different. xs t a continuous-time signal an impulse train zero except at nT x n a discrete-time sequence time normalization no explicit information about sampling rate Many-to-many in general not invertible 6 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY