matlab實(shí)驗(yàn)指導(dǎo)

1、數(shù)字信號(hào)處理MATLAB實(shí)驗(yàn)指導(dǎo)實(shí)驗(yàn)一：離散時(shí)間信號(hào)和離散時(shí)間系統(tǒng) 一、 實(shí)驗(yàn)?zāi)康模?、 以MATLAB為工具學(xué)習(xí)離散時(shí)間信號(hào)的圖形表示；2、 以課本提供的例程，練習(xí)、理解典型離散信號(hào)及其基本運(yùn)算；3、 通過MATLAB仿真簡單的離散時(shí)間系統(tǒng)，研究其時(shí)域特性；4、 加深對(duì)離散系統(tǒng)的差分方程、沖激響應(yīng)和卷積分析方法的理解。二、 實(shí)驗(yàn)內(nèi)容：1、 典型序列的產(chǎn)生與顯示；2、 序列的簡單運(yùn)算；3、 復(fù)合和復(fù)雜信號(hào)的產(chǎn)生與顯示；4、 離散時(shí)間系統(tǒng)的仿真：線性和非線性系統(tǒng)、時(shí)變和非時(shí)變系統(tǒng)的仿真；5、 線性時(shí)不變離散時(shí)間系統(tǒng)：系統(tǒng)沖激響應(yīng)、卷積運(yùn)算、系統(tǒng)的級(jí)聯(lián)、系統(tǒng)的穩(wěn)定性；三、 實(shí)驗(yàn)例程： 1、 參照課

2、本例程產(chǎn)生下列序列，并用plot、stem好人subplot命令繪出其圖形：單位取樣序列；單位階躍序列；矩形序列RN(n)，斜變序列。所需輸入的數(shù)據(jù)是產(chǎn)生序列的長度L和抽樣頻率FT。% Program P1_1% Generation of a Unit Sample Sequence clf;% Generate a vector from -10 to 20n = -10:20;% Generate the unit sample sequenceu = zeros(1,10) 1 zeros(1,20);% Plot the unit sample sequencestem(n,u);x

3、label(Time index n);ylabel(Amplitude);title(Unit Sample Sequence);axis(-10 20 0 1.2);2、 編寫MATLAB實(shí)指數(shù)序列程序，% Program P1_3% Generation of a real exponential sequenceclf;n = 0:35; a = 1.2; K = 0.2;x = K*a.n;stem(n,x);xlabel(Time index n);ylabel(Amplitude);3、 編寫產(chǎn)生swept frequency sinusoidal 序列的程序。% Program

4、 P1_7% Generation of a swept frequency sinusoidal sequencen = 0:100;a = pi/2/100;b = 0;arg = a*n.*n + b*n;x = cos(arg);clf;stem(n, x);axis(0,100,-1.5,1.5);title(Swept-Frequency Sinusoidal Signal);xlabel(Time index n);ylabel(Amplitude);grid; axis; 4、 產(chǎn)生正弦振幅調(diào)制序列% Generation of amplitude modulated sequ

5、enceclf;n = 0:100; m = 0.4;fH = 0.1; fL = 0.01; xH = sin(2*pi*fH*n);xL = sin(2*pi*fL*n);y = (1+m*xL).*xH;stem(n,y);grid;xlabel(Time index n);ylabel(Amplitude);5、 用滑動(dòng)平均濾波器平滑帶噪信號(hào)，討論濾波器長度對(duì)平滑效果、輸出平滑后信號(hào)與輸入帶噪信號(hào)之間延時(shí)的影響。% Program P1_5% Signal Smoothing by Averagingclf;R = 51;d = 0.8*(rand(R,1) - 0.5); % Gen

6、erate random noisem = 0:R-1;s = 2*m.*(0.9.m); % Generate uncorrupted signalx = s + d; % Generate noise corrupted signalsubplot(2,1,1);plot(m,d,r-,m,s,g-,m,x,b-.);xlabel(Time index n);ylabel(Amplitude);legend(dn ,sn ,xn );x1 = 0 0 x;x2 = 0 x 0;x3 = x 0 0;y = (x1 + x2 + x3)/3;subplot(2,1,2);plot(m,y(2

7、:R+1),r-,m,s,g-);legend( yn ,sn );xlabel(Time index n);ylabel(Amplitude);6、編寫輸入序列、計(jì)算輸出序列、差分輸出并畫出輸出序列。% Program P2_4% Generate the input sequencesclf;n = 0:40; D = 10;a = 3.0;b = -2;x = a*cos(2*pi*0.1*n) + b*cos(2*pi*0.4*n);xd = zeros(1,D) x;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.75;ic = 0 0; % Se

8、t initial conditions% Compute the output yny = filter(num,den,x,ic);% Compute the output ydnyd = filter(num,den,xd,ic);% Compute the difference output dnd = y - yd(1+D:41+D);% Plot the outputssubplot(3,1,1)stem(n,y);ylabel(Amplitude); title(Output yn); grid;subplot(3,1,2)stem(n,yd(1:41);ylabel(Ampli

9、tude);title(Output due to Delayed Input xn ?, num2str(D),); grid;subplot(3,1,3)stem(n,d);xlabel(Time index n); ylabel(Amplitude);title(Difference Signal); grid;7、 編寫輸入序列和系統(tǒng)單位脈沖響應(yīng)的卷積程序并畫出圖形。% Program P2_7clf;h = 3 2 1 -2 1 0 -4 0 3; % impulse responsex = 1 -2 3 -4 3 2 1; % input sequencey = conv(h,x)

10、;n = 0:14;subplot(2,1,1);stem(n,y);xlabel(Time index n); ylabel(Amplitude);title(Output Obtained by Convolution); grid;x1 = x zeros(1,8);y1 = filter(h,1,x1);subplot(2,1,2);stem(n,y1);xlabel(Time index n); ylabel(Amplitude);title(Output Generated by Filtering); grid;8、 編寫輸入信號(hào)經(jīng)濾波形成的系統(tǒng)輸出信號(hào)。% Program P2

11、_9% Generate the input sequenceclf;n = 0:299;x1 = cos(2*pi*10*n/256);x2 = cos(2*pi*100*n/256);x = x1+x2;% Compute the output sequencesnum1 = 0.5 0.27 0.77;y1 = filter(num1,1,x); % Output of System #1den2 = 1 -0.53 0.46;num2 = 0.45 0.5 0.45;y2 = filter(num2,den2,x); % Output of System #2% Plot the ou

12、tput sequencessubplot(2,1,1);plot(n,y1);axis(0 300 -2 2);ylabel(Amplitude);title(Output of System #1); grid;subplot(2,1,2);plot(n,y2);axis(0 300 -2 2);xlabel(Time index n); ylabel(Amplitude);title(Output of System #2); grid;9、四、本實(shí)驗(yàn)用到的matlab命令Stem plot sin abs cos conv clf subplot filter impz 實(shí)驗(yàn)二：時(shí)域連

13、續(xù)時(shí)間信號(hào)和頻域抽樣理論的驗(yàn)證與觀察 一、實(shí)驗(yàn)?zāi)康模?、理解并掌握信號(hào)時(shí)域采樣和頻率抽樣理論涉及的過程和效果；2、通過編程加深理解奈奎斯特采樣定理，理解不滿足采樣條件的對(duì)時(shí)域和頻域采樣造成的混疊現(xiàn)象。二、實(shí)驗(yàn)內(nèi)容：1、時(shí)域的采樣過程、采樣定理和混疊效果；2、頻域中的采樣效果；3、學(xué)習(xí)buttworth模擬低通濾波器的設(shè)計(jì)命令；三、實(shí)驗(yàn)例程1、 連續(xù)時(shí)間信號(hào)的理想抽樣及其混疊效果clf;T = 0.4;f = 25;n = (0:T:1);xs = cos(2*pi*f*n);t = linspace(-0.5,1.5,500);ya = sinc(1/T)*t(:,ones(size(n) -

14、 (1/T)*n(:,ones(size(t)*xs;plot(n,xs,o,t,ya);grid;xlabel(Time, msec);ylabel(Amplitude);title(Reconstructed continuous-time signal y_a(t);axis(0 1 -1.2 1.2)2、.頻率抽樣及其混疊效果clf;t = 0:0.002:50;xa = 2*t.*exp(-t);subplot(4,2,1)plot(t,xa);gridxlabel(Time, msec);ylabel(Amplitude);title(Continuous-time signal

15、x_a(t);subplot(4,2,2)wa = 0:10/511:10;ha = freqs(2,1 2 1,wa);plot(wa/(2*pi),abs(ha);grid;xlabel(Frequency, kHz);ylabel(Amplitude);title(|X_a(jOmega)|);axis(0 5/pi 0 2);subplot(4,2,3)T = 1;n = 0:T:10;xs = 2*n.*exp(-n);k = 0:length(n)-1;stem(k,xs);grid;xlabel(Time index n);ylabel(Amplitude);title(Disc

16、rete-time signal xn);subplot(4,2,4)wd = 0:pi/255:pi;hd = freqz(xs,1,wd);plot(wd/(T*pi), T*abs(hd);grid;xlabel(Frequency, kHz);ylabel(Amplitude);title(|X(ejomega)|);axis(0 1/T 0 2)3、buttworth模擬低通濾波器的設(shè)計(jì)命令并畫出該濾波器圖形。clf;Fp = 3500;Fs = 4500;Wp = 2*pi*Fp; Ws = 2*pi*Fs;N, Wn = buttord(Wp, Ws, 0.5, 30,s);b,

17、a = butter(N, Wn, s);wa = 0:(3*Ws)/511:3*Ws;h = freqs(b,a,wa);plot(wa/(2*pi), 20*log10(abs(h);gridxlabel(Frequency, Hz);ylabel(Gain, dB);title(Gain response);axis(0 3*Fs -60 5);四、本實(shí)驗(yàn)用到的matlab命令Butter buttord freqs freqz sinc hist實(shí)驗(yàn)三：離散時(shí)間信號(hào)與離散時(shí)間系統(tǒng)系統(tǒng)的頻域分析 一、 實(shí)驗(yàn)?zāi)康模?、 掌握matlab 編寫基于離散時(shí)間傅立葉變換（DTFT）、z變換和離散

18、傅立葉變換（DFT）的程序，并通過本訓(xùn)練加深對(duì)這些概念和算法的理解；2、 理解DTFT、ZT和DFT的相互關(guān)系。3、 掌握離散系統(tǒng)的頻率響應(yīng)分析；4、 理解零、極點(diǎn)分布的概念。 5、理解帕斯瓦爾定理。二、實(shí)驗(yàn)內(nèi)容：1、 離散時(shí)間傅立葉變換（DTFT）的定義、計(jì)算和基本性質(zhì)；2、 Z變換分析；3、 系統(tǒng)傳輸函數(shù)和頻率響應(yīng)；4、 系統(tǒng)傳輸函數(shù)的類型；5、 系統(tǒng)穩(wěn)定性測(cè)試；6、 離散傅立葉變換（DFT）的計(jì)算和基本性質(zhì)；7、 利用FFT實(shí)現(xiàn)線性卷積； 8、 利用FFT顯示理解帕斯瓦爾定理。三、實(shí)驗(yàn)例程1、用MATLAB編寫離散時(shí)間信號(hào)的傅里葉變換（DTFT）并繪出8點(diǎn)幅頻和相頻曲線。% Progra

19、m P3_1% Evaluation of the DTFT clf;% Compute the frequency samples of the DTFTw = -4*pi:8*pi/511:4*pi;num = 2 1;den = 1 -0.6;h = freqz(num, den, w);% Plot the DTFTsubplot(2,1,1)plot(w/pi,real(h);gridtitle(Real part of H(ejomega)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)plot(w/pi,imag(h);grid

20、title(Imaginary part of H(ejomega)xlabel(omega /pi);ylabel(Amplitude);pausesubplot(2,1,1)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum |H(ejomega)|)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)plot(w/pi,angle(h);gridtitle(Phase Spectrum argH(ejomega)xlabel(omega /pi);ylabel(Phase in radians);2、

21、MATLAB驗(yàn)證實(shí)序列的離散時(shí)間傅立葉變換的對(duì)稱關(guān)系。N = 8;k = 0:N-1;gamma = 0.5;x = exp(gamma*k);y = exp(gamma*fliplr(k);xev =0.5*(zeros(1,N-1) x+y zeros(1,N-1);xod = 0.5*(zeros(1,N-1) x-y zeros(1,N-1);X,w = freqz(x,1,512);Xev,w = freqz(xev,1,512);Xod,w = freqz(xod,1,512);Xev = exp(j*w*(N-1).*Xev;Xod = exp(j*w*(N-1).*Xod;%

22、Verify real(X)= Xev, and imag(X)= Xodr = 0:511;w0 = -pi*r/512;X1 = freqz(x,1,w0);% Verify X = conj(X1)% real(X)= real(X1) and imag(X)= -imag(X1)% abs(X)= abs(X1) and angle(X)= -angle(X1)3、 用MATLAB計(jì)算序列Modulation Property of DTFT并給出其調(diào)制圖形。% Program P3_5% Modulation Property of DTFTclf;w = -pi:2*pi/255:

23、pi;x1 = 1 3 5 7 9 11 13 15 17;x2 = 1 -1 1 -1 1 -1 1 -1 1;y = x1.*x2;h1 = freqz(x1, 1, w);h2 = freqz(x2, 1, w);h3 = freqz(y,1,w);subplot(3,1,1)plot(w/pi,abs(h1);gridtitle(Magnitude Spectrum of First Sequence)subplot(3,1,2)plot(w/pi,abs(h2);gridtitle(Magnitude Spectrum of Second Sequence)subplot(3,1,3

24、)plot(w/pi,abs(h3);gridtitle(Magnitude Spectrum of Product Sequence)4、用MATLAB計(jì)算序列的N點(diǎn)離散傅立葉變換，N取3，5，7,9。比較在時(shí)計(jì)算得到的離散時(shí)間傅立葉變換的結(jié)果。N = 16;clf;N = input(The value of N = );k = -N:N;y1=ones(1,2*N+1);y2=y1-abs(k)/N;w = 0:2*pi/255:2*pi;Y2 = freqz(y2, 1, w);Y2dft = fft(y2);k = 0:1:2*N;plot(w/pi,abs(Y2),k*2/(2*N

25、+1),abs(Y2dft),o);xlabel(Normalized frequency);ylabel(Amplitude);4、用MATLAB研究濾波器的系統(tǒng)函數(shù)及其沖激響應(yīng)，產(chǎn)生零極點(diǎn)圖，最終顯示出零點(diǎn)的位置。clf;b = 1 -8.5 30.5 -63;num1 = b 81 fliplr(b);num2 = b 81 81 fliplr(b);num3 = b 0 -fliplr(b);num4 = b 81 -81 -fliplr(b);n1 = 0:length(num1)-1;n2 = 0:length(num2)-1;subplot(2,2,1); stem(n1,num

26、1);xlabel(Time index n);ylabel(Amplitude); grid;title(Type 1 FIR Filter);subplot(2,2,2); stem(n2,num2);xlabel(Time index n);ylabel(Amplitude); grid;title(Type 2 FIR Filter);subplot(2,2,3); stem(n1,num3);xlabel(Time index n);ylabel(Amplitude); grid;title(Type 3 FIR Filter);subplot(2,2,4); stem(n2,num

27、4);xlabel(Time index n);ylabel(Amplitude); grid;title(Type 4 FIR Filter);pausesubplot(2,2,1); zplane(num1,1);title(Type 1 FIR Filter);subplot(2,2,2); zplane(num2,1);title(Type 2 FIR Filter);subplot(2,2,3); zplane(num3,1);title(Type 3 FIR Filter);subplot(2,2,4); zplane(num4,1);title(Type 4 FIR Filter

28、);disp(Zeros of Type 1 FIR Filter are);disp(roots(num1);disp(Zeros of Type 2 FIR Filter are);disp(roots(num2);disp(Zeros of Type 3 FIR Filter are);disp(roots(num3);disp(Zeros of Type 4 FIR Filter are);disp(roots(num4);4. 用MATLAB產(chǎn)生序列的圓周移位,并畫圖觀察該現(xiàn)象，clf;x = 0 2 4 6 8 10 12 14 16;N = length(x)-1; n = 0:

29、N;y = circshift(x,5);XF = fft(x);YF = fft(y);subplot(2,2,1)stem(n,abs(XF);gridtitle(Magnitude of DFT of Original Sequence);subplot(2,2,2)stem(n,abs(YF);gridtitle(Magnitude of DFT of Circularly Shifted Sequence);subplot(2,2,3)stem(n,angle(XF);gridtitle(Phase of DFT of Original Sequence);subplot(2,2,4

30、)stem(n,angle(YF);gridtitle(Phase of DFT of Circularly Shifted Sequence);5、 用MATLAB編寫快速傅里葉變換，并實(shí)現(xiàn)偶序列的DFT的虛實(shí)部，采用圖形表示。% Program P3_11% Relations between the DFTs of the Periodic Even% and Odd Parts of a Real Sequencex = 1 2 4 2 6 32 6 4 2 zeros(1,247);x1 = x(1) x(256:-1:2);xe = 0.5 *(x + x1);XF = fft(x

31、);XEF = fft(xe);clf;k = 0:255;subplot(2,2,1);plot(k/128,real(XF); grid;ylabel(Amplitude);title(Re(DFTxn);subplot(2,2,2);plot(k/128,imag(XF); grid;ylabel(Amplitude);title(Im(DFTxn);subplot(2,2,3);plot(k/128,real(XEF); grid;xlabel(Time index n);ylabel(Amplitude);title(Re(DFTx_en);subplot(2,2,4);plot(k

32、/128,imag(XEF); grid;xlabel(Time index n);ylabel(Amplitude);title(Im(DFTx_en);6、 編寫穩(wěn)定性測(cè)試程序% Program P4_4% Stability Testclf;den = input(Denominator coefficients = );ki = poly2rc(den);disp(Stability test parameters are);disp(ki);7、用MATLABD 編寫基于FFT的帕斯瓦爾定理。% Program P3_12% Parsevals Relationx = (1:128)

33、 (128:-1:1);XF = fft(x);a = sum(x.*x)b = round(sum(abs(XF).2)/256)四、本實(shí)驗(yàn)用到的matlab命令filter Freqz impz filrfilt residuez tf2zp zp2sos zplane fft sinc zplane 實(shí)驗(yàn)四：IIR&FIR數(shù)字濾波器的設(shè)計(jì)一、 實(shí)驗(yàn)?zāi)康模?、熟悉無限沖激響應(yīng)（IIR）和有限沖激響應(yīng)（FIR）網(wǎng)絡(luò)結(jié)構(gòu)，對(duì)比學(xué)習(xí)模擬濾波器和數(shù)字濾波器的常用指標(biāo)；2、熟悉沖激響應(yīng)不變法和雙線性變換法設(shè)計(jì)低通濾波器的程序編寫，并深化理解；3、熟悉FIR線性相位濾波器的概念及其表示；4、熟悉FIR

34、濾波器窗函數(shù)設(shè)計(jì)法；5、熟悉兩種濾波器設(shè)計(jì)過程，并可修改其設(shè)計(jì)指標(biāo)，對(duì)比輸出效果。二、實(shí)驗(yàn)內(nèi)容：1、IIR(無限沖激響應(yīng)濾波器)階數(shù)估計(jì)及其buttworth和chybyshev濾波器設(shè)計(jì)；2、沖激響應(yīng)不變法和雙線性變換法設(shè)計(jì)；3、FIR濾波器設(shè)計(jì)中出現(xiàn)頻域出現(xiàn)吉布斯現(xiàn)象的來由；3、有限沖激響應(yīng)濾波器窗函數(shù)設(shè)計(jì)法；三、實(shí)驗(yàn)計(jì)算及例程1、設(shè)低通DF的3dB帶寬頻率wc=0.2,止帶頻率ws=0.4,在 w=ws處的止帶衰減20lg|H(ejws)|=-15dB,試用脈沖響應(yīng)不變法（沖激不變法）設(shè)計(jì)一個(gè)Butterworth低通DF。(設(shè)采樣頻率fs=20kHz） Wp=input(Normali

35、zed passband edge =);Ws=input(Normalized stopband edge =);Rp=input(Passband ripple in dB =);Rs=input(Minimum stopband attenuation in dB =);N,Wn=buttord (Wp,Ws,Rp,Rs);b,a=butter(N,W n);h,omega=freqz(b,a,512);plot(omega/pi,20*log10(abs(h);grid;xlabel(omega/pi);ylabel(Gain dB);title(IIR Butterworth Low

36、pass Filter);2無限沖激響應(yīng)濾波器階數(shù)估計(jì)和濾波器設(shè)計(jì) 巴特沃茲帶阻濾波器Ws = 0.4 0.6; Wp = 0.2 0.8; Rp = 0.4; Rs = 50;% Estimate the Filter OrderN1, Wn1 = buttord(Wp, Ws, Rp, Rs); % Design the Filternum,den = butter(N1,Wn1,stop); % Display the transfer functiondisp(Numerator Coefficients are );disp(num);disp(Denominator Coeffic

37、ients are );disp(den);% Compute the gain responseg, w = gain(num,den); % Plot the gain responseplot(w/pi,g);grid axis(0 1 -60 5);xlabel(omega /pi); ylabel(Gain in dB);title(Gain Response of a Butterworth Bandstop Filter)3、吉布斯環(huán)的生成； 在FIR窗函數(shù)設(shè)計(jì)法中，頻域傅立葉變換的無限振蕩諧波數(shù)列疊加合成時(shí)，會(huì)產(chǎn)生尖銳不連續(xù)的區(qū)間，好比方波的下降及上升，這就是吉布斯現(xiàn)象，這種現(xiàn)

38、象產(chǎn)生的不僅與諧波的疊加合成的數(shù)量有關(guān)，而且其變化的寬度隨合成的個(gè)數(shù)增加而變窄。單位方波： 傅立葉級(jí)數(shù)表示： function y = gibbs(x,M,duty)% GIBBS% x： 待估價(jià)的值 (0x0.5)% M： 區(qū)間% duty：占空比(0-1)%if (nargin3) duty = 0.5;endp = (-M:M);for (j=1:length(x) y(j) = sum(duty*sinc(duty*p).*exp(-i*2*pi*p*abs(x(j);end正規(guī)重構(gòu)：覆蓋整個(gè)單位方波范圍s = linspace(-0.5,0.5,200);plot(s,gibbs(s

39、,M);4、有限沖激響應(yīng)濾波器階數(shù)估計(jì)和濾波器設(shè)計(jì)； 用凱塞窗設(shè)計(jì)一FIR低通濾波器，低通邊界頻率 ，阻帶邊界頻率 ，阻帶衰減 不小于50dB。 計(jì)算與例程由過渡帶寬和阻帶衰減 來決定凱塞窗的N和 凱塞窗設(shè)計(jì)對(duì)應(yīng)的MATLAB程序?yàn)椋?wn=kaiser(30,4.55); nn=0:1:29; alfa=(30-1)/2; hd=sin(0.4*pi*(nn-alfa)./(pi*(nn-alfa); h=hd.*wn; h1,w1=freqz(h,1); plot(w1/pi,20*log10(abs(h1); axis(0,1,-80,10); grid;xlabel(歸一化頻率/p) ylabel(幅度/dB) 5、試用雙線性變換法設(shè)計(jì)Butterworth低通DF。已知低通DF的3dB帶寬頻率，止帶起始頻率，在 處的止帶衰減要求進(jìn)行計(jì)算機(jī)MATLAB仿真并得出結(jié)果。解：使用Matlab軟件仿真仿真的程序如下： clc;clear all;OmegaP=2*pi*2