Ch2_课件new_c_培训课件.pptVIP

§2.5 The Sampling Process If the unit of sampling period T is in seconds The unit of normalized digital angular frequency ?0 is radians/sample The unit of normalized analog angular frequency ?0 is radians/second The unit of analog frequency f0 is hertz (Hz) Plots of these sequences (shown with circles) and their parent time functions are shown below: Note that each sequence has exactly the same sample value for any given n The above phenomenon of a continuous-time signal of higher frequency acquiring the identity of a sinusoidal sequence of lower frequency after sampling is called aliasing Homework Problems 2.3， 2.4(b)， 2.17， 2.21(a),(c), 2.22，2.41，2.43(只须做x[n] )，2.51 MATLAB Exercise M 2.1, M 2.2, M 2.4, M 2.6 In down-sampling by an integer factor M 1, every M-th samples of the input sequence are kept and M-1 in-between samples are removed: y[n]=x[nM] An example of the down-sampling operation ( Down-sampling factor M=3 ) The time-reversal operation on a finite- length sequence is obtained using the modulo operation Let 0,1,…,N-1 be a set of N positive integers and let m be any integer. The integer r obtained by evaluating modulo operation r= mN= m modulo N is called the residue，an integer with a value between 0 and N-1 r=m+lN where l is a positive or negative integer chosen to make m+lN an integer between 0 and N-1 〔2.3节内容衔接5.4节（圆周卷积）和5.5节（序列分类）〕 2.3 Operations on Finite-Length Sequences  2.3.1 Circular Time-Reversal Operation The circular time-reversal version {y[n]} of a length-N sequence {x[n]} defined for 0 ≤ n ≤ N-1 is given by { y[n]}={x[-nN]} Example – Consider {x[n]}={x[0], x[1], x[2], x[3], x[4]} Its circular time-reversed version is given by {y[n]}={x[-n5]} ( length N=5 ) ={x[0], x[4], x[3], x[2], x[1]} The circular shift operation for a finite- length sequence is defined using the modulo operation Let x[n] be a length-N sequenc