通信原理ppt课件-class-four

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,2014/4/20,#,Principles of Communications,Lecturer:Dr.Xuechen Chen,School of Mobile Information Engineering,Sun Yat-Sen University,Chapter 4:Digitization of Analog Signal,Principles of CommunicationsLe,1,2,Chapter 4,Digitization,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),2Chapter 4 Digitization of ana,2,Digital Communication System,Digital Communication System,3,Topics to be covered,Topics to be covered,4,5,4.2,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,f,H,and if it is sampled by periodic impulses with interval time,T,1/2,f,H,then,s,(,t,)can be completely decided by these samples.,54.2 Sampling of analog signal,5,6,Proof of sampling theorem,Let:,s,(,t,),signal with highest frequency less than,f,H,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,s,k,(,t,)is,S,k,(,f,),then,where,S,k,(,f,),spectrum of,s,k,(,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,6Proof of sampling theorem,6,A fast varying signal should be sampled more frequently!,Theoretically governed by the Nyquist sampling theorem,The,ideal,low pass filter,is unable to be achieved.The cut-off edge of a practical filter can not be so sharp.Therefore,the practical sampling rate,f,s,must be much larger than,2,f,H,.,For,example,the highest frequency of typical telephone signal is limited to 3,400 Hz,and the sampling frequency used is 8,000 Hz.,A fast varying signal should b,7,8,4.2.2,Sampling of band-pass analog signal,The frequency band of a band-pass signal is limited to between,f,L,and,f,H,i.e.,the cut-off frequency of its frequency spectrum at the lower end is obviously larger than 0,.,The required sampling frequency,f,s,:,where,B,signal bandwidth,n,largest integer less than,f,H,/,B,0,k,1,。,84.2.2 Sampling of band-pass,8,9,4.2.3,Analog pulse modulation,PAM,PDM,PPM,（,a,）,Baseband signal(,b,)PAM signal,(,c,)PDM signal(,d,)PPMsignal,Figure 4.2.6 Analog pulse modulation,94.2.3 Analog pulse modulatio,9,10,4.3,Quantization of sampled,signal,4.3.1,Principles of quantization,Purpose of quantization:,To,digitize the sampled signal,.,Quantization is a rounding process,each sampled signal point is rounded to the“nearest”value from a finite set of possible quantization levels.,10 4.3 Quantization of samp,10,图,4.3.1,抽样信号的量化,Method of quantization,:,Let,s,(,kT,)be the sampled value,.,If,N,bits of binary symbols are,used to express it,then only,M,=,2,N,different,sampled values,can be expressed,.,There are totally,M,discrete levels.They are called quantization level,.,The method of representing continuous samples by,M,quantition levels is called quantization,.,Example:in the figure,It is uniform quantization in the figure,.,图4.3.1 抽样信号的量化Method of quanti,11,Performance Measure of Quantization,Quantization noise:,Average(mean square error)Noise:,Signal-to-quantization noise ratio,(SQNR):,Performance Measure of Quanti,12,13,4.3.2,Uniform,quantization,Assume:the magnitude of the analog samples is within,a,b,and the number of quantization levels,M,then the quantization interval is:,the boundary points are:,If quantized output level,q,i,is the midpoint of the quantization,interval,then,134.3.2 Uniform quantization,13,14,Find average power of quantization noise,N,q,：,where,s,k,is sample of signal,i.e.,s,(,kT,),s,q,is magnitude of quantized signal,i.e.,s,q,(,kT,),f,(,s,k,)is probability density of signal sample,s,k,E,expresses operation of statistical mean.,M,is number of quantization levels,Find average power of signal,s,k,:,Average signal to quantization noise power ratio can be found from the above,two,equations,.,14Find average power of quanti,14,通信原理ppt课件-class-four,15,Original file,Quantized at 4 bits,Quantized at 6 bits,Original file Quantized at 4 b,16,17,【Example 4.1】Assume the number of quantization levels for a uniform quantizer is,M,and the sample of the input signal has uniform probability density in the interval-,a,a,.Find the average signal to quantization noise ratio for the quantizer.,Solution:,from eq.(4.3-5),we have,或,17【Example 4.1】Assume the numb,17,18,4.3.2 Non,u,niform,quantization,Disadvantage,of uniform quantization,:,1.the,quantization noise,N,q,is constant,.,2.real audio signals(speech and music)are more concentrated near zero.,3.Human ear is more sensitive to quantization errors at small values.,Why we need Nonuniform quantization?,Nonuniform,quantiza