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1、Matlab Worksheet 3 Part A 1. Using function conv_m.m to make convolution between the following to functions (x and h): x=3, 11, 7, 0, -1, 7, -5, 0, 2; h=11, 9, 0, -7, -3, 2, 0 -1; nx=-2:6; nh=0:7; Plot the functions and convolution results. Answer: home_work_3_A_1.m x=3, 11, 7, 0, -1, 7, -5, 0, 2; h
2、=11, 9, 0, -7, -3, 2, 0 -1; nx=-2:6; nh=0:7; y, ny=conv_m(x,nx,h,nh); subplot(3,1,1); stem(nx,x); ylabel(xn); axis(-6 10 -20 20); subplot(3,1,2); stem(nh,h); ylabel(hn); axis(-6 10 -20 20); subplot(3,1,3); stem(ny,y); xlabel(n); ylabel(yn); axis(-6 10 -50 50); conv_m.m function y, ny=conv_m(x,nx,h,n
3、h) %convolution function %conv_m.m nyb=nx(1)+nh(1); nye=nx(length(x)+nh(length(h); ny=nyb:nye; y=conv(x,h); end -6-4-20246810 -20 0 20 xn -6-4-20246810 -20 0 20 hn -6-4-20246810 -50 0 50 n yn 2 2. Plot the frequency response over for the following transfer function by letting 0 , where is the freque
4、ncy (rad/sample)., with appropriate labels and title. j ez . 9 . 06 . 1 )( 2 zz z zH Answer: home_work_3_A_2.m delta=0.01; Omega=0:delta:pi; z=exp(j .* Omega); H= z ./ (z.2+1.6*z+0.9); subplot(2,1,1); plot(Omega, abs(H),m,LineWidth,2); xlabel(0Omegapi); ylabel(|H(Omega)|); axis(0 pi 0 max(abs(H); su
5、bplot(2,1,2); plot(Omega,atan2(imag(H),real(H),k,LineWidth,2); xlabel(0Omegapi); ylabel( -pi Phi_H pi) title( frequency response); axis(0 pi -pi pi); 00.511.522.53 0 5 10 15 0 |H()| 00.511.522.53 -2 0 2 0 - H frequency response 3. Use fft to analyse following signal by plotting the original signal a
6、nd its spectrum. . 1024 4672sin 1024 1372sin 1024 322sin nnn nx 3 Answer: home_work_3_A_3.m %Examine signal components %sampling rate 1024Hz N=1024; dt=1/N; t=0:dt:1-dt; %*define the signal* x= sin(2*pi*32 .*t) +sin(2*pi*137 .*t )+ sin(2*pi* 467 .*t ) ; %* subplot(2,1,1); plot(t,x); axis(0 1 -1 1);
7、xlabel(nT (seconds); ylabel(xn); X=fft(x); df=1; f=0:df:N-1; subplot(2,1,2); plot(f,abs(X); axis(0 N/2 0 120); xlabel(k (Hz); ylabel(|Xk|); 00.10.20.30.40.50.60.70.80.91 -1 -0.5 0 0.5 1 nT (seconds) xn 050100150200250300350400450500 0 50 100 k (Hz) |Xk| 4. Use the fast Fourier transform function fft
8、 to analyse following signal. Plot the original signal, and the magnitude of its spectrum linearly and logarithmically. Apply Hamming window to reduce the leakage. . 1024 7 .4672sin 1024 4 . 1372sin 1024 5 .322sin nnn nx The hamming window can be coded in Matlab as for n=1:N hamming(n)=0.54+0.46*cos
9、(2*n-N+1)*pi/N); end; 4 where N is the data length in the FFT. Answer: home_work_3_A_4.m %Windowing for reducing leakage %sampling rate 1024Hz N=1024; dt=1/N; t=0:dt:1-dt; %*define the signal* x= sin(2*pi*32.5.*t )+. sin(2*pi*137.4 .*t )+. sin(2*pi*467.7.*t ); %* % Apply rectangular window subplot(3
10、,2,1); plot(t,x); axis(0 1 -5 5); xlabel(nT (seconds); ylabel(xn rectang win); X=fft(x); df=1; f=0:df:N-1; subplot(3,2,2); plot(f,20*log10(abs(X); axis(0 N/2 -30 60); xlabel(k (Hz); ylabel(|Xk| (db); % Apply triangular window for n=1:N w(n)=1-abs(2*n-N+1)/N; end; x1=x .*w; subplot(3,2,3); plot(t,x1)
11、; axis(0 1 -5 5); xlabel(nT (seconds); ylabel(xn triang win); X=fft(x1); df=1; f=0:df:N-1; subplot(3,2,4); plot(f,20*log10(abs(X); axis(0 N/2 -30 60); xlabel(k (Hz); ylabel(|Xk| (db); % Apply Hamming window for n=1:N w(n)=0.54+0.46*cos(2*n-N+1)*pi/N); end; x1=x .*w; subplot(3,2,5); plot(t,x1); axis(
12、0 1 -5 5); xlabel(nT (seconds); ylabel(xn Hamming win); X=fft(x1); df=1; f=0:df:N-1; subplot(3,2,6); plot(f,20*log10(abs(X); 5 axis(0 N/2 -30 60); xlabel(k (Hz); ylabel(|Xk| (db); 00.51 -5 0 5 nT (seconds) xn rectang win 0200400 -20 0 20 40 60 k (Hz) |Xk| (db) 00.51 -5 0 5 nT (seconds) xn triang win
13、 0200400 -20 0 20 40 60 k (Hz) |Xk| (db) 00.51 -5 0 5 nT (seconds) xn Hamming win 0200400 -20 0 20 40 60 k (Hz) |Xk| (db) 6 Part B Simulation Using SIMULINK INTRODUCTION The objective of this laboratory is to learn about various properties of signals and systems by doing simulations in SIMULINK. PAR
14、T 1. BASICS OF SIMULINK 1.1 UNDERSTANDING SIMPLE WAVEFORMS AND INTEGRATION Create a pulse of height 2 units from time 0 to 4 seconds by subtracting two unit steps and adding a gain. Connect this pulse to an integrator with a gain of 0.5 and a zero initial condition. Connect oscilloscopes to show the
15、 pulse and the output of the integrator. You may wish to name your simulation (block) diagram; to do so use the save as feature under edit. Your block diagram should be similar as below. u Before simulating you need to pull down the simulation header and double click on parameters. Unless told otherwise always assume that you can use the ode 45 integration algorithm shown in this window and the other default par
