實(shí)驗(yàn)三 模擬-數(shù)字轉(zhuǎn)換

1、實(shí)驗(yàn)三 模擬-數(shù)字轉(zhuǎn)換一、實(shí)驗(yàn)預(yù)習(xí)： 1.概述 2.Huffman編碼 3.量化4.均勻PCM平按已量化值的遞增次序映射。5.非均勻PCM二、實(shí)驗(yàn)內(nèi)容（題目解答）：1. 編碼實(shí)驗(yàn)代碼：主函數(shù)：clc;p=0.2 0.15 0.13 0.12 0.1 0.09 0.08 0.07 0.06;h,l=huffman(p);H=entropy(p);求熵函數(shù)：function h=entropy(p)if length(find(p<0)=0, error('Not a prob. vector, negative component(s)')endif abs(sum(p)-

2、1)>10e-10, error('Not a prob. vector, components do not add up to 1')endh=sum(-p.*log2(p);Huffman編碼函數(shù)：function h,l=huffman(p); if length(find(p<0)=0, error('Not a prob. vector, negative component(s)')endif abs(sum(p)-1)>10e-10, error('Not a prob. vector, components do no

3、t add up to 1')endn=length(p);q=p;m=zeros(n-1,n);for i=1:n-1 q,l=sort(q); m(i,:)=l(1:n-i+1),zeros(1,i-1); q=q(1)+q(2),q(3:n),1;endfor i=1:n-1 c(i,:)=blanks(n*n);endc(n-1,n)='0'c(n-1,2*n)='1'for i=2:n-1 c(n-i,1:n-1)=c(n-i+1,n*(find(m(n-i+1,:)=1). -(n-2):n*(find(m(n-i+1,:)=1); c(n-

4、i,n)='0' c(n-i,n+1:2*n-1)=c(n-i,1:n-1); c(n-i,2*n)='1' for j=1:i-1 c(n-i,(j+1)*n+1:(j+2)*n)=c(n-i+1,. n*(find(m(n-i+1,:)=j+1)-1)+1:n*find(m(n-i+1,:)=j+1); endendfor i=1:n h(i,1:n)=c(1,n*(find(m(1,:)=i)-1)+1:find(m(1,:)=i)*n); l1(i)=length(find(abs(h(i,:)=32);endl=sum(p.*l1);實(shí)驗(yàn)結(jié)果：Huff

5、man編碼結(jié)果：平均碼長(zhǎng)：信源的熵：2. 量化實(shí)驗(yàn)代碼：主函數(shù)：echo on ;a=-20,-5,-4,-3,-2,-1,0,1,2,3,4,5,20;y,dist=mse_dist('normal',a,0.01,0,1);for i=1:length(a)-1 y(i)=centroid('normal',a(i),a(i+1),0.001,0,1); echo off ;end子函數(shù)：function dist=uq_mdpnt(funfcn,b,n,delta,tol,p1,p2,p3) if (2*b<delta*(n-1) error(

6、9;Too many levels for this range.'); returnendargs=;for j=1:nargin-5 args=args,',p',int2str(j);endargs=args,')'a(1)=-b;a(n+1)=b;a(2)=-(n/2-1)*delta;y(1)=a(2)-delta/2;for i=3:n a(i)=a(i-1)+delta; y(i-1)=a(i)-delta/2;endy(n)=a(n)+delta;dist=0;for i=1:n newfun = 'x_a2_fnct'

7、; dist=dist+eval('quad(newfun,a(i),a(i+1),tol,funfcn,', num2str(y(i), args);endfunction y,dist=uq_dist(funfcn,b,c,n,delta,s,tol,p1,p2,p3) if (c-b<delta*(n-2) error('Too many levels for this range.'); returnendif (s<b) error('The leftmost boundary too small.'); returnend

8、if (s+(n-2)*delta>c) error('The leftmost boundary too large.'); returnendargs=;for j=1:nargin-7 args=args,',p',int2str(j);endargs=args,')'a(1)=b;for i=2:n a(i)=s+(i-2)*delta;enda(n+1)=c;y,dist=eval('mse_dist(funfcn,a,tol',args);實(shí)驗(yàn)結(jié)果：均方誤差：dist = 0.0769量化值：y = -5.016

9、8 -4.2168 -3.2605 -2.3158 -1.3832 -0.4599 0.4599 1.3832 2.3158 3.2605 4.2168 5.01683. 均勻PCM 實(shí)驗(yàn)代碼：主函數(shù)：echo ont=0:0.01:10;a=sin(t);sqnr8,aquan8,code8=u_pcm(a,8);sqnr16,aquan16,code16=u_pcm(a,16);pause % Press a key to see the SQNR for N=8.sqnr8pause % Press a key to see the SQNR for N=16.sqnr16pause %

10、 Press a key to see the first five quantized values.plot(t,a,'-',t,aquan8,'-',t,aquan16,'-',t,zeros(1,length(t);title('用8電平和16電平對(duì)一個(gè)正弦信號(hào)進(jìn)行的均勻PCM'); 子函數(shù)：function sqnr,a_quan,code=u_pcm(a,n)amax=max(abs(a);a_quan=a/amax;b_quan=a_quan;d=2/n;q=d.*0:n-1;q=q-(n-1)/2)*d;for i

11、=1:n a_quan(find(q(i)-d/2 <= a_quan) & (a_quan <= q(i)+d/2)=. q(i).*ones(1,length(find(q(i)-d/2 <= a_quan) & (a_quan <= q(i)+d/2); b_quan(find( a_quan=q(i) )=(i-1).*ones(1,length(find( a_quan=q(i) );enda_quan=a_quan*amax;nu=ceil(log2(n);code=zeros(length(a),nu);for i=1:length(a)

12、for j=nu:-1:0 if ( fix(b_quan(i)/(2j) = 1) code(i,(nu-j) = 1; b_quan(i) = b_quan(i) - 2j; end endendsqnr=20*log10(norm(a)/norm(a-a_quan); 實(shí)驗(yàn)結(jié)果： 所得的SQNR是：sqnr8 = 18.9023 sqnr16 = 25.1272 4. 非均勻PCM 實(shí)驗(yàn)代碼： 主函數(shù)：echo ont=0:0.01:10;a=20*randn(1,20),randn(1,480);n=64;sqnr,aquan,code=u_pcm(a,64);pause % Pres

13、s a key to see the SQNR .sqnrpause plot(a);pauseplot(aquan,'-');sqnr1,aquan1,code1=mula_pcm(a,64,255);pause % Press a key to see the SQNR .sqnr1pause plot(aquan1,'-');子函數(shù)：function sqnr,a_quan,code=mula_pcm(a,n,mu)y,maximum=mulaw(a,mu);sqnr,y_q,code=u_pcm(y,n);a_quan=invmulaw(y_q,mu);

14、a_quan=maximum*a_quan;sqnr=20*log10(norm(a)/norm(a-a_quan);function sqnr,a_quan,code=u_pcm(a,n)amax=max(abs(a);a_quan=a/amax;b_quan=a_quan;d=2/n;q=d.*0:n-1;q=q-(n-1)/2)*d;for i=1:n a_quan(find(q(i)-d/2 <= a_quan) & (a_quan <= q(i)+d/2)=. q(i).*ones(1,length(find(q(i)-d/2 <= a_quan) &

15、; (a_quan <= q(i)+d/2); b_quan(find( a_quan=q(i) )=(i-1).*ones(1,length(find( a_quan=q(i) );enda_quan=a_quan*amax;nu=ceil(log2(n);code=zeros(length(a),nu);for i=1:length(a) for j=nu:-1:0 if ( fix(b_quan(i)/(2j) = 1) code(i,(nu-j) = 1; b_quan(i) = b_quan(i) - 2j; end endendsqnr=20*log10(norm(a)/no

16、rm(a-a_quan);實(shí)驗(yàn)結(jié)果：sqnr = 19.7348sqnr1 = 24.1075三、實(shí)驗(yàn)分析與討論1.信號(hào)量化的目的是什么？ 用有限的離散值近似模擬原始信號(hào)的振幅，在接收端由這些有限的離散值恢復(fù)原始信號(hào) 。2.量化信號(hào)有哪些優(yōu)缺點(diǎn)？缺點(diǎn)：無論抽樣值大小如何，量化噪聲的均方根值都是固定不變的。因此，當(dāng)信號(hào)較小時(shí)，則信號(hào)量化噪聲功率比也比較小，這樣，對(duì)于弱信號(hào)時(shí)的信號(hào)量噪比就難以達(dá)到給定的要求。3.什么是A率壓縮和率壓縮？它們各自有什么特點(diǎn)？ A壓縮律是指符合下式的對(duì)數(shù)壓縮規(guī)律： 律壓縮特性： 4. 在PCM系統(tǒng)中，信號(hào)量噪比是指什么，它和信號(hào)帶寬有什么關(guān)系？ 信號(hào)功率與量化噪聲之比

17、簡(jiǎn)稱信號(hào)量噪聲比。 當(dāng)?shù)屯ㄐ盘?hào)最高頻率給定時(shí)，PCM系統(tǒng)的輸出信號(hào)量噪比隨系統(tǒng)的帶寬B按指數(shù)規(guī)律增長(zhǎng)。四、思考題1、實(shí)驗(yàn)1中Huffman碼的效率是多少？Huffman碼唯一嗎？為什么？答：霍夫曼編碼效率等于熵/平均碼長(zhǎng)，已知熵為3.0371，平均碼長(zhǎng)為3.1，所以霍夫曼編碼效率為0.98。霍夫曼碼不唯一，因?yàn)樵谶M(jìn)行概率相加時(shí)，可能會(huì)出現(xiàn)上一次的和與某一個(gè)概率一樣，此時(shí)有向上和向下兩種編碼方式，因此造成霍夫曼碼不唯一。2、.答：3、答：代碼：%均勻PCM量化器n=input('請(qǐng)輸入量化級(jí)數(shù):');endtime = 2;%定義信號(hào)周期為2dt = 0.5; %定義抽樣間隔為0

18、.5t = 0:dt:endtime; %劃分?jǐn)?shù)組a = zeros(size(t);for tt=1:1/dt a(tt+0:endtime/2-1*(2/dt)=t(tt); %當(dāng)0<=t<1時(shí)，x(t)=tendfor tt=1/dt+1:2/dt a(tt+0:endtime/2-1*(2/dt)=2-t(tt); %當(dāng)1<=t<2時(shí)，x(t)=-t+2endamax=max(abs(a); %max求最大值，abs求絕對(duì)值a_quan=a/amax; %歸一化b_quan=a_quan; %賦初值d=1/n; %求出量化間隔q=d.*1:n;q=q-d/2; %求出量化電平%進(jìn)行量化for i=1:n%定位第i個(gè)量化間隔碼子 a_quan(find(q(i)-d/2<=a_quan) & (a_quan<=q(i)+d/2)=.?q(i).*ones(1,length(find(q(i)-d/2<=a_quan)&(a_quan<=q(i)+d/2); %賦值為相應(yīng)的量化電平b_quan(find(a_quan=q(i) =(i-1) .* ones(1,length(find(a_quan=q(i);enda_quan=a_quan*am