Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.341:DISCRETE-TIME SIGNAL PROCESSING OpenCourse Ware 2006 Lecture 5 Sampling Rate Conversion Reading:Section 4.6 in Oppenheim,Schafer Buck (OSB). It is often necessary to change the sampling rate of a discrete-time signal to obtain a new discrete-time representation of the underlying continuous-time signal.The desired system is shown below: xn] wn] xn xc(t) fi→f2 D/C C/D w回→ 入 万=1 f=2 Sample rate converter Sampling Rate Compression by an Integer Factor To reduce the sampling rate of a sequence by an integer factor,the sequence can be further compressed or decimated as depicted in OSB Figure 4.20.This discrete-time sampler can be interpreted as the cascade of a D/C converter and a C/D converter in which: xn]=xc(nT), Idln]=x[nM]=Ic(nMT). The discrete-time Fourier transform of x[n]and raln]are xe=-x((号-) xe=ax(”-)》Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.341: Discrete-Time Signal Processing OpenCourseWare 2006 Lecture 5 Sampling Rate Conversion Reading: Section 4.6 in Oppenheim, Schafer & Buck (OSB). It is often necessary to change the sampling rate of a discrete-time signal to obtain a new discrete-time representation of the underlying continuous-time signal. The desired system is shown below: x[n] - f1 → f2 -w[n] ⇐⇒ x[n] - D/C - xc(t) C/D - w[n] 6 6 f1 = 1 T 1 f1 = 1 T 2 Sample rate converter Sampling Rate Compression by an Integer Factor To reduce the sampling rate of a sequence by an integer factor, the sequence can be further compressed or decimated as depicted in OSB Figure 4.20. This discrete-time sampler can be interpreted as the cascade of a D/C converter and a C/D converter in which: x[n] = xc(nT) , xd[n] = x[nM] = xc(nMT). The discrete-time Fourier transform of x[n] and xd[n] are X(ejω) = 1 �∞ −∞ Xc � j �ω 2πk�� , T k= T − T 1 � ω 2πr �� Xd(ejω) = �∞ −∞ Xc � j . MT r= MT − MT 1