通信原理(英文版)4课件.ppt

Chapter 4 Digitiation of analog signal 4.1 Introduction Two categories of information sources: analog signal, digital signal Three steps of A/D conversion: sampling, quantization , coding Most popular A/D conversion method: Pulse Code Modulation (PCM) 4.2 Sampling of analog signal 4.2.1 Sampling of low-pass analog signal Usually sampling at equal time interval T Theoretically, sampling process ＝ periodical unit impulse ? analog signal Practically, sampling process ＝ periodical narrow pulse ? analog signal Sampling theorem: If the highest frequency of a continuous analog signal s(t) is less than fH , and if it is sampled by periodic impulses with interval time T ? 1/2fH , then s(t) can be completely decided by these samples. Proof of sampling theorem Let: s(t) － signal with highest frequency less than fH ?T(t) － periodical unit impulse with repetition period T and repetition frequency fs = 1/T, then the sampled signal is: Let the Fourier transform of sk(t) is Sk(f), then where, Sk(f) － spectrum of sk(t) S(f) － spectrum of s(t) ??( f ) － spectrum of ?T(t) ??(f ) is the frequency spectrum of periodical unit impulse, it can be found as Substituting into obtain The above equation shows that spectrum Sk(f) of the sampled signal is the superposition of infinite spectra S(f) with frequency interval fs, since S(f - nfs) is the result of displacement nfs of the signal frequency spectrum S(f) on the frequency axis. The highest frequency of signal s(t) has been assumed less than fH, therefore if frequency interval fs ? 2fH, then each displaced spectrum S(f) of the original signal contained in Sk(f) is not superposed with each other, as shown in the figure. Thus frequency spectrum S(f) of signal s(t) can be separated from Sk(f), and s(t) can be easily obtained from S(f), i.e. the original signal can be restored from the sampled sig