1、數(shù)字信號(hào)處理MATLAB上機(jī)作業(yè)M 2.21. 題目The square wave and the sawtooth wave are two periodic sequences as sketched in figure P2.4.Using the function stem. The input data specified by the user are: desired length L of the sequence, peak value A, and the period N. For the square wave sequence an additional user-s

2、pecified parameter is the duty cycle, which is the percent of the period for which the signal is positive. Using this program generate the first 100 samples of each of the above sequences with a sampling rate of 20 kHz ,a peak value of 7, a period of 13 ,and a duty cycle of 60% for the square wave.

3、2. 程序% 用戶定義各項(xiàng)參數(shù)參數(shù)A = input('The peak value =');L = input('Length of sequence =');N = input('The period of sequence =');FT = input('The desired sampling frequency =');DC = input('The square wave duty cycle = ');% 產(chǎn)生所需要的信號(hào)t = 0:L-1;T = 1/FT;x = A*sawtooth(2*pi*t

4、/N);y = A*square(2*pi*(t/N),DC);% Plotsubplot(2,1,1)stem(t,x);ylabel('幅度');xlabel('n');subplot(2,1,2)stem(t,y);ylabel('幅度');xlabel('n');3. 結(jié)果4. 結(jié)果分析M 2.41. 題目(a) Write a matlab program to generate a sinusoidal sequence xn= Acos(0 n+) and plot the sequence using the st

5、em function. The input data specified by the user are the desired length L, amplitude A, the angular frequency 0 , and the phase where 0<0 <pi and 0<=<=2pi. Using this program generate the sinusoidal sequences shown in figure 2.15.(b) Generate sinusoidal sequences with the angular freque

6、ncies given in Problem 2.22. Determine the period of each sequence from the plot and verify the result theoretically.2. 程序%用戶定義的參數(shù)L = input('Desired length = ');A = input('Amplitude = ');omega = input('Angular frequency = ');phi = input('Phase = ');%信號(hào)產(chǎn)生n = 0:L-1;x =

7、A*cos(omega*n + phi);stem(n,x);xlabel('n');ylabel('幅度');title('omega_o = ',num2str(omega);3. 結(jié)果(a)0=00=0.10=0.80=1.2(b)0=0.140=0.240=0.340=0.680=0.754. 結(jié)果分析M 2.51. 題目Generate the sequences of problem 2.21(b) to 2.21(e) using matlab.2. 程序(b)n = 0 : 99;x=sin(0.6*pi*n+0.6*pi);st

8、em(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)

9、+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');3. 結(jié)果(b) (c) (d) (e) (f) 4. 結(jié)果分析M 2.61. 題目Write a matlab program to plot a continuous-time sinusoidal signal and its sampled version and verif

10、y figure 2.19. You need to use the hold function to keep both plots.2. 程序%用戶定義的參數(shù)fo = input('Frequency of sinusoid in Hz = ');FT = input('Samplig frequency in Hz = ');%產(chǎn)生信號(hào)t = 0:0.001:1;g1 = cos(2*pi*fo*t);plot(t,g1,'-')xlabel('時(shí)間t');ylabel('幅度')holdn = 0:1:FT

11、;gs = cos(2*pi*fo*n/FT);plot(n/FT,gs,'o');hold off3. 結(jié)果4. 結(jié)果分析M 3.11. 題目Using program 3_1 determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT for various values of r and :Gej=11-2rcose-j+r2e-2j , 0<r<1.2. 程序%program 3_1%discrete-tim

12、e fourier transform computatition%k=input('Number of frequency points = ');num=input('Numerator coefficients= ');den=input('Denominator coefficients= ');%computer the frequency responsew=0:pi/k:pi;h=freqz(num,den,w);%plot the frequency responsesubplot(221)plot(w/pi,real(h);gr

13、idtitle('real part')xlabel('omega/pi');ylabel('Amplitude')subplot(222)plot(w/pi,imag(h);gridtitle('imaginary part')xlabel('omega/pi');ylabel('Amplitude')subplot(223)plot(w/pi,abs(h);gridtitle('magnitude spectrum')xlabel('omega/pi');ylab

14、el('magnitude')subplot(224)plot(w/pi,angle(h);gridtitle('phase spectrum')xlabel('omega/pi');ylabel('phase,radians')3. 結(jié)果(a) r=0.8 =/6(b) r=0.6 = /3 4. 結(jié)果分析M 3.41. 題目Using matlab verify the following general properties of the DTFT as listed in Table 3.2:(a) Linearity,

15、(b) time-shifting, (c) frequency-shifting, (d) differentiation-in-frequency, (e) convolution, (f) modulation, and (g) Parsevals relation. Since all data in matlab have to be finite-length vectors, the sequences to be used to verify the properties are thus restricted to be of finite length.2. 程序%先定義兩

16、個(gè)信號(hào)N = input('The length of the sequence = ');k = 0:N-1;%g為正弦信號(hào)g = 2*sin(2*pi*k/(N/2);%h為余弦信號(hào)h = 3*cos(2*pi*k/(N/2);G,w = freqz(g,1);H,w = freqz(h,1);%*% 線性性質(zhì)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(

17、'|Y(ejomega)|');title('線性疊加后的頻率特性');grid;% 畫出 Y 的頻率特性subplot(212),plot(w/pi,alpha*abs(G)+beta*abs(H);xlabel('omega/pi');ylabel('alpha|G(ejomega)|+beta|H(ejomega)|');title('線性疊加前的頻率特性');grid;% 畫出alpha*G+beta*H 的頻率特性%*% 時(shí)移性質(zhì)n0 = 10;%時(shí)移10個(gè)的單位y2 = zeros(1,n0) g;Y2

18、,w = freqz(y2,1);G0 = exp(-j*w*n0).*G;figure(2);subplot(211),plot(w/pi,abs(G0);xlabel('omega/pi');ylabel('|G0(ejomega)|');title('G0的頻率特性');grid;% 畫出 G0的頻率特性subplot(212),plot(w/pi,abs(Y2);xlabel('omega/pi');ylabel('|Y2(ejomega)|');title('Y2的頻率特性');grid;

19、% 畫出Y2 的頻率特性%*% 頻移特性w0 = pi/2; % 頻移pi/2r=256; %the value of w0 in terms of number of samplesk = 0:N-1;y3 = g.*exp(j*w0*k);Y3,w = freqz(y3,1);% 對(duì)采樣的512個(gè)點(diǎn)分別進(jìn)行減少pi/2,從而生成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(&

20、#39;|Y3(ejomega)|');title('Y3的頻率特性');grid;% 畫出 Y3的頻率特性subplot(212),plot(w/pi,abs(G1);xlabel('omega/pi');ylabel('|G1(ejomega)|');title('G1的頻率特性');grid;% 畫出G1 的頻率特性%*% 頻域微分k = 0:N-1;y4 = k.*g;Y4,w = freqz(y4,1);%在頻域進(jìn)行微分y0 = (-1).k).*g;G2 = G(2:512)' sum(y0)'

21、delG = (G2-G)*512/pi;figure(4);subplot(211),plot(w/pi,abs(Y4);xlabel('omega/pi');ylabel('|Y4(ejomega)|');title('Y4的頻率特性');grid;% 畫出 Y4的頻率特性subplot(212),plot(w/pi,abs(delG);xlabel('omega/pi');ylabel('|delG(ejomega)|');title('delG的頻率特性');grid;% 畫出delG的頻率

22、特性%*% 相乘性質(zhì)y5 = conv(g,h);%時(shí)域卷積Y5,w = freqz(y5,1);figure(5);subplot(211),plot(w/pi,abs(Y5);xlabel('omega/pi');ylabel('|Y5(ejomega)|');title('Y5的頻率特性');grid;% 畫出 Y5的頻率特性subplot(212),plot(w/pi,abs(G.*H);%頻域乘積xlabel('omega/pi');ylabel('|G.*H(ejomega)|');title('

23、;G.*H的頻率特性');grid;% 畫出G.*H的頻率特性%*% 帕斯瓦爾定理y6 = g.*h;%對(duì)于freqz函數(shù)，在0到2pi直接取樣Y6,w = freqz(y6,1,512,'whole');G0,w = freqz(g,1,512,'whole');H0,w = freqz(h,1,512,'whole');% Evaluate the sample value at w = pi/2% and verify with Y6 at pi/2H1 = fliplr(H0(1:129)') fliplr(H0(130:

24、512)')'val = 1/(512)*sum(G0.*H1);% Compare val with Y6(129) i.e sample at pi/2% Can extend this to other points similarly% Parsevals theoremval1 = sum(g.*conj(h);val2 = sum(G0.*conj(H0)/512;% Comapre val1 with val23. 結(jié)果(a)(b)(c)(d)(e)4. 結(jié)果分析M 3.81. 題目Using matlab compute the N-point DFTs of

25、the length-N sequences of Problem 3.12 for N=3, 5, 7, and 10. Compare your results with that obtained by evaluating the DTFTs computed in Problem 3.12 at = 2pik/N, k=0, 1,N-1.2. 程序%用戶定義N的長(zhǎng)度N = input('The value of N = ');k = -N:N;y1 = ones(1,2*N+1);w = 0:2*pi/255:2*pi;Y1 = freqz(y1, 1, w);%對(duì)y

26、1做傅里葉變換Y1dft = fft(y1);k = 0:1:2*N;plot(w/pi,abs(Y1),k*2/(2*N+1),abs(Y1dft),'o');grid;xlabel('歸一化頻率');ylabel('幅度');(a) clf;N = input('The value of N = ');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)

27、,k*2/(2*N+1),abs(Y1dft),'o');xlabel('Normalized frequency');ylabel('Amplitude');(b) %用戶定義N的長(zhǎng)度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);%對(duì)y1做傅里葉變換Y2dft = fft(y2);k = 0:1:2*N;plot(w/pi,abs(Y2),

28、k*2/(2*N+1),abs(Y2dft),'o');grid;xlabel('歸一化頻率');ylabel('幅度');(c) %用戶定義N的長(zhǎng)度N = input('The value of N = ');k = -N:N;y3 =cos(pi*k/(2*N);w = 0:2*pi/255:2*pi;Y3 = freqz(y3, 1, w);%對(duì)y1做傅里葉變換Y3dft = fft(y3);k = 0:1:2*N;plot(w/pi,abs(Y3),k*2/(2*N+1),abs(Y3dft),'o');g

29、rid;xlabel('歸一化頻率');ylabel('幅度');3. 結(jié)果(a) N=3 N=5 N=7 N=10 (b) N=3 N=5 N=7 N=10 (c) N=3 N=5 N=7 N=10 4. 結(jié)果分析M 3.191. 題目Using Program 3_10 determine the z-transform as a ratio of two polynomials in z-1 from each of the partial-fraction expansions listed below:(a) X1z=-2+104+z-1-82+z-1

30、 , z>0.5,(b) X2z=3.5-21-0.5z-1-3+z-11-0.25z-2 , z>0.5,(c) X3z=53+2z-12-43+2z-1+31+0.81z-2 , z>0.9,(d) X4z=4+105+2z-1+z-16+5z-1+z-2 , z>0.5.2. 程序% Program 3_10% Partical-Fraction Expansion to rational z-Transform%r = input('Type in the residues = ');p = input('Type in the poles = ');k = input('Type in the constants = ');num, den = residuez(r,p,k);disp('Numberator polynominal coefficients');disp(num)disp('Denominator polynomial coefficients&