数字信号处理上机实验报告

数字信号处理上机实验报告2018年5月21日 M2.2题目ThesquarewaveandthesawtoothwavearetwoperiodicsequencesassketchedinfigureP2.4.Usingthefunctionstem.Theinputdataspecifiedbytheuserare:desiredlengthLofthesequence,peakvalueA,andtheperiodN.Forthesquarewavesequenceanadditionaluser-specifiedparameteristhedutycycle,whichisthepercentoftheperiodforwhichthesignalispositive.Usingthisprogramgeneratethefirst100samplesofeachoftheabovesequenceswithasamplingrateof20kHz,apeakvalueof7,aperiodof13,andadutycycleof60%forthesquarewave.程序clc;closeall;f=20000;%采样频率L=100*(1/f);%采样个数A=7;%最大值N=13;%周期t=0:1/20000:L-1/20000;%t=0:1:20;y1=(A*sawtooth(2*pi/N*f*t));m=(A-max(y1))/2;y2=m+y1;figure(1);subplot(2,1,1);stem(t,y2);y3=square(2*pi/13*20000*t,60);subplot(2,1,2)stem(t,y3);结果M2.4题目Writeamatlabprogramtogenerateasinusoidalsequencex[n]=Acos(ω0n+Ф)andplotthesequenceusingthestemfunction.TheinputdataspecifiedbytheuserarethedesiredlengthL,amplitudeA,theangularfrequencyω0,andthephaseФwhere0<ω0<piand0<=Ф<=2pi.Usingthisprogramgeneratethesinusoidalsequencesshowninfigure2.15.GeneratesinusoidalsequenceswiththeangularfrequenciesgiveninProblem2.22.Determinetheperiodofeachsequencefromtheplotandverifytheresulttheoretically.程序clc;clearall;closeall;L=input('Desiredlength=');A=input('Amplitude=');omega=input('Angularfrequency=');phi=input('Phase=');%信号产生n=0:L-1;x=A*cos(omega*n+phi);stem(n,x);xlabel('n');ylabel('幅度');title(['\omega_{o}=',num2str(omega)]);结果ω0=0ω0=0.1πω0=0.8πω0=1.2πω0=0.14πω0=0.24πω0=0.34πω0=0.68πω0=0.75πM2.5题目Generatethesequencesofproblem2.21(b)to2.21(e)usingmatlab.程序(b)n=0:99;x=sin(0.6*pi*n+0.6*pi);stem(n,x);xlabel('n');ylabel('幅度');(c)n=0:99;x=2*cos(1.1*pi*n-0.5*pi)+2*sin(0.7*pi*n);stem(n,x);xlabel('n');ylabel('幅度');(d)n=0:99;x=3*sin(1.3*pi*n-4*cos(0.3*pi*n+0.45*pi));stem(n,x);xlabel('n');ylabel('幅度');(e)n=0:99;x=5*sin(1.2*pi*n+0.65*pi)+4*sin(0.8*pi*n)-cos(0.8*pi*n);stem(n,x);xlabel('n');ylabel('幅度');(f)n=0:99;x=mod(n,6);stem(n,x);xlabel('n');ylabel('幅度');结果(b)(c)(d)(e)(f)M2.6题目Writeamatlabprogramtoplotacontinuous-timesinusoidalsignalanditssampledversionandverifyfigure2.19.Youneedtousetheholdfunctiontokeepbothplots.程序clc;closeall;clearall;fre_sin=input('FrequencyofsinusoidinHz=');fre_sample=input('SampligfrequencyinHz=');t=0:0.001:1;g=cos(2*pi*fre_sin*t);plot(t,g,'-')xlabel('时间t');ylabel('幅度')holdn=0:1:fre_sample;g_samle=cos(2*pi*fre_sin*n/fre_sample);plot(n/fre_sample,g_sample,'x');holdoff结果频率10Hz;采样频率500Hz.M3.1题目Usingprogram3_1determineandplottherealandimaginarypartsandthemagnitudeandphasespectraofthefollowingDTFTforvariousvaluesofrandθ:Gejω=程序clc;closeall;clearall;%采样频率k=1000;r=input('r=');theda=input('theda=');%num多项式分子系数%den多项式分母系数num=[1,0,0];den=[1,-2*r*cos(theda),r^2];w=0:pi/k:pi;h=freqz(num,den,w);subplot(221)plot(w/pi,real(h));gridon;title('realpart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(222)plot(w/pi,imag(h));gridon;title('imaginarypart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(223)plot(w/pi,abs(h));gridon;title('magnitudespectrum')xlabel('\omega/\pi');ylabel('magnitude')subplot(224)plot(w/pi,angle(h));gridon;title('phasespectrum')xlabel('\omega/\pi');ylabel('phase,radians')结果r=0.8θ=π/6r=0.6θ=π/3M3.4题目UsingmatlabverifythefollowinggeneralpropertiesoftheDTFTaslistedinTable3.2:(a)Linearity,(b)time-shifting,(c)frequency-shifting,(d)differentiation-in-frequency,(e)convolution,(f)modulation,and(g)Parseval’srelation.Sincealldatainmatlabhavetobefinite-lengthvectors,thesequencestobeusedtoverifythepropertiesarethusrestrictedtobeoffinitelength.程序clc;clearall;closeall;N=input('Thelengthofthesequence=');k=0:N-1;%g为正弦信号g=2*sin(2*pi*k/(N/2));%h为余弦信号h=3*cos(2*pi*k/(N/2));[G,w]=freqz(g,1);[H,w]=freqz(h,1);%线性性质alpha=0.5;beta=0.25;y=alpha*g+beta*h;[Y,w]=freqz(y,1);figure(1);subplot(211),plot(w/pi,abs(Y));xlabel('\omega/\pi');ylabel('|Y(e^j^\omega)|');title('线性叠加后的频率特性');grid;%画出Y的频率特性subplot(212),plot(w/pi,alpha*abs(G)+beta*abs(H));xlabel('\omega/\pi');ylabel('\alpha|G(e^j^\omega)|+\beta|H(e^j^\omega)|');title('线性叠加前的频率特性');grid;%画出alpha*G+beta*H的频率特性%时移性质n0=10;%时移10个的单位y2=[zeros([1,n0])g];[Y2,w]=freqz(y2,1);G0=exp(-j*w*n0).*G;figure(2);subplot(211),plot(w/pi,abs(G0));xlabel('\omega/\pi');ylabel('|G0(e^j^\omega)|');title('G0的频率特性');grid;%画出G0的频率特性subplot(212),plot(w/pi,abs(Y2));xlabel('\omega/\pi');ylabel('|Y2(e^j^\omega)|');title('Y2的频率特性');grid;%画出Y2的频率特性%频移特性w0=pi/2;%频移pi/2r=256;%thevalueofw0intermsofnumberofsamplesk=0:N-1;y3=g.*exp(j*w0*k);[Y3,w]=freqz(y3,1);%对采样的512个点分别进行减少pi/2,从而生成G(exp(w-w0))k=0:511;w=-w0+pi*k/512;G1=freqz(g,1,w);figure(3);subplot(211),plot(w/pi,abs(Y3));xlabel('\omega/\pi');ylabel('|Y3(e^j^\omega)|');title('Y3的频率特性');grid;%画出Y3的频率特性subplot(212),plot(w/pi,abs(G1));xlabel('\omega/\pi');ylabel('|G1(e^j^\omega)|');title('G1的频率特性');grid;%画出G1的频率特性%频域微分k=0:N-1;y4=k.*g;[Y4,w]=freqz(y4,1);%在频域进行微分y0=((-1).^k).*g;G2=[G(2:512)'sum(y0)]';delG=(G2-G)*512/pi;figure(4);subplot(211),plot(w/pi,abs(Y4));xlabel('\omega/\pi');ylabel('|Y4(e^j^\omega)|');title('Y4的频率特性');grid;%画出Y4的频率特性subplot(212),plot(w/pi,abs(delG));xlabel('\omega/\pi');ylabel('|delG(e^j^\omega)|');title('delG的频率特性');grid;%画出delG的频率特性%相乘性质y5=conv(g,h);%时域卷积[Y5,w]=freqz(y5,1);figure(5);subplot(211),plot(w/pi,abs(Y5));xlabel('\omega/\pi');ylabel('|Y5(e^j^\omega)|');title('Y5的频率特性');grid;%画出Y5的频率特性subplot(212),plot(w/pi,abs(G.*H));%频域乘积xlabel('\omega/\pi');ylabel('|G.*H(e^j^\omega)|');title('G.*H的频率特性');grid;%画出G.*H的频率特性%帕斯瓦尔定理y6=g.*h;%对于freqz函数，在0到2pi直接取样[Y6,w]=freqz(y6,1,512,'whole');[G0,w]=freqz(g,1,512,'whole');[H0,w]=freqz(h,1,512,'whole');H1=[fliplr(H0(1:129)')fliplr(H0(130:512)')]';val=1/(512)*sum(G0.*H1);val1=sum(g.*conj(h));val2=sum(G0.*conj(H0))/512;结果(a)(b)(c)(d)(e)M3.8题目UsingmatlabcomputetheN-pointDFTsofthelength-NsequencesofProblem3.12forN=3,5,7,and10.CompareyourresultswiththatobtainedbyevaluatingtheDTFTscomputedinProblem3.12atω=2pik/N,k=0,1,……N-1.程序clc;clearall;closeall;N=input('ThevalueofN=');k=-N:N;y1=ones([1,2*N+1]);w=0:2*pi/255:2*pi;Y1=freqz(y1,1,w);Y1dft=fft(y1);k=0:1:2*N;plot(w/pi,abs(Y1),k*2/(2*N+1),abs(Y1dft),'x');gridon;xlabel('Normalizedfrequency');ylabel('Amplitude');clc;clearall;closeall;N=input('ThevalueofN=');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);%对y1做傅里叶变换Y2dft=fft(y2);k=0:1:2*N;plot(w/pi,abs(Y2),k*2/(2*N+1),abs(Y2dft),'x');gridon;xlabel('Normalizedfrequency');ylabel('Amplitude');clc;clearall;closeall;N=input('ThevalueofN=');k=-N:N;y3=cos(pi*k/(2*N));w=0:2*pi/255:2*pi;Y3=freqz(y3,1,w);Y3dft=fft(y3);k=0:1:2*N;plot(w/pi,abs(Y3),k*2/(2*N+1),abs(Y3dft),'x');gridon;xlabel('Normalizedfrequency');ylabel('Amplitude');结果N=3N=5N=7N=10N=3N=5N=7N=10N=3N=5N=7N=10M3.19题目UsingProgram3_10determinethez-t