數(shù)字信號處理(DSP)實驗報告

1、數(shù)字信號處理(DSP)實驗報告 學 院 電子科學與工程學院 姓 名 學 號 指導教師 2016年6月2日實驗一M2.1 Write a MATLAB program to the generate the conjugate-symmetric and conjugate-antisymmetric parts of a finite length complex sequence. Using this program verify the results of Example 2.8.Code:x = 0 1+4j -2+3j 4-2j -5-6j -2j 3;cs = 0.5*(x +

2、conj(fliplr(x);ca = 0.5*(x - conj(fliplr(x);M2.2 (a) Using Program 2-2, generate the sequences shown in Figures 2.23 and 2.24. (b)Generate and plot the complex exponential sequence -2.7e(-0.4+j6)n for 0n82 using Program 2-2.Code:% Program 2_2% Generation of complex exponential sequence%a = input(Typ

3、e in real exponent = );b = input(Type in imaginary exponent = );c = a + b*i;K = input(Type in the gain constant = );N = input (Type in length of sequence = );n = 1:N;x = K*exp(c*n);%Generate the sequencestem(n,real(x);%Plot the real partxlabel(Time index n);ylabel(Amplitude);title(Real part);disp(PR

4、ESS RETURN for imaginary part);pausestem(n,imag(x);%Plot the imaginary partxlabel(Time index n);ylabel(Amplitude);title(Imaginary part);Figure 2.23Figure 2.24Figure 2.2bM2.4 (a) Write a MATLAB program to generate a sinusoidal sequence xn=Asin(w0n+f), and plot the sequence using the stem function. Th

5、e input data specified by the user the desired length L, amplitude A, the angular frequency w0, and the phase f where 0w0 and 0 2. Using this program, generate the sinusoidal sequences shown in Figure 2.22. (b) Generate sinusoidal sequences with the angular frequencies given in Problem 2.40. Determi

6、ne the period of each sequence from the plot, and verify the result theoretically.Code:L = input(Desired length = );A = input(Amplitude = );omega = input(Angular frequency = );phi = input(Phase = );n = 0:L-1;x = A*cos(omega*n + phi);stem(n,x);xlabel(Time Index); ylabel(Amplitude);title(omega_o = ,nu

7、m2str(omega/pi),pi);Figure 2.22M2.6 Write a MATLAB program to plot a continuous-time sinusoidal signal and its sampled version, and verify Figure 2.28. You need to the hold function to keep both plots.Code:t = 0:0.001:1;fo = input(Frequency of sinusoid in Hz = );FT = input(Sampling frequency in Hz =

8、 );g1 = cos(2*pi*fo*t);plot(t,g1,:);xlabel(time); ylabel(Amplitude); holdn = 0:1:FT;gs = cos(2*pi*fo*n/FT);plot(n/FT,gs,o); hold offM3.2 Using Program 3-1, determine and plot the real and imaginary parts and the magnitude and phase spectra of the DTFTs of the sequence of Problem 3.18 for N=10.,Code:

9、% Program 3_1% Discrete-Time Fourier Transform Computation% Read in the desired number of frequency samplesk = input(Number of frequency points = );% Read in the numerator and denominator coefficientsnum = input(Numerator coefficients = );den = input(Denominator coefficients = );% Compute the freque

10、ncy responsew = 0:pi/(k-1):pi;h = freqz(num, den, w);%h = h.*exp(1i*w*10);% Plot the frequency response%h=sin(21*w/2)./sin(w/2);%h=exp(-1i*w*5).*sin(w*11/2)./sin(w/2);subplot(2,2,1)plot(w/pi,real(h);gridtitle(Real part)xlabel(omega/pi); ylabel(Amplitude)subplot(2,2,2)plot(w/pi,imag(h);gridtitle(Imag

11、inary part)xlabel(omega/pi); ylabel(Amplitude)subplot(2,2,3)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum)xlabel(omega/pi); ylabel(Magnitude)subplot(2,2,4)plot(w/pi,angle(h);gridtitle(Phase Spectrum)xlabel(omega/pi); ylabel(Phase, radians)M3.3 Using Program 3-1, determine and plot the real and imagi

12、nary parts and the magnitude and phase spectra of the following DTFTs:(a)X(ej)=0.1323(1+0.1444e-j-0.4519e-j2+0.1444e-j3+e-j4)1+0.1386e-j+0.8258e-j2+0.1393e-j3+0.4153e-j4 ,(b) X(ej)=0.3192(1+0.1885e-j-0.1885e-j2-e-j3)1+0.7856e-j+1.4654e-j2-0.2346e-j3 .Code: % Program 3_1% Discrete-Time Fourier Transf

13、orm Computation% Read in the desired number of frequency samplesk = input(Number of frequency points = );% Read in the numerator and denominator coefficientsnum = input(Numerator coefficients = );den = input(Denominator coefficients = );% Compute the frequency responsew = 0:pi/(k-1):pi;h = freqz(num

14、, den, w);%h = h.*exp(1i*w*10);% Plot the frequency response%h=sin(21*w/2)./sin(w/2);%h=exp(-1i*w*5).*sin(w*11/2)./sin(w/2);subplot(2,2,1)plot(w/pi,real(h);gridtitle(Real part)xlabel(omega/pi); ylabel(Amplitude)subplot(2,2,2)plot(w/pi,imag(h);gridtitle(Imaginary part)xlabel(omega/pi); ylabel(Amplitu

15、de)subplot(2,2,3)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum)xlabel(omega/pi); ylabel(Magnitude)subplot(2,2,4)plot(w/pi,angle(h);gridtitle(Phase Spectrum)xlabel(omega/pi); ylabel(Phase, radians)Figure aFigure bM3.4 Using MATLAB, verify the symmetry relations of the DTFT of a real sequence as liste

16、d in Table 3.1.Code:N = 8; % Number of samples in sequencegamma = 0.5; k = 0:N-1;x = 0.5.k;w = -3*pi:pi/1024:3*pi;X = freqz(x,1,w);subplot(2,2,1)plot(w/pi,real(X);gridtitle(Real part)xlabel(omega/pi); ylabel(Amplitude)subplot(2,2,2)plot(w/pi,imag(X);gridtitle(Imaginary part)xlabel(omega/pi); ylabel(

17、Amplitude)subplot(2,2,3)plot(w/pi,abs(X);gridtitle(Magnitude Spectrum)xlabel(omega/pi); ylabel(Magnitude)subplot(2,2,4)plot(w/pi,angle(X);gridtitle(Phase Spectrum)xlabel(omega/pi); ylabel(Phase, radians)M4.1 Using Program 4-1(new), investigate the effect of signal smoothing by a moving-average filte

18、r of length 5, 7 and 9. Does the signal smoothing improve with an increase in the length? What is the effect of the length on the delay between the smoothing output and the noisy input?Code:% Program 4_1% Signal Smoothing by a Moving-Average FilterR = 50;d = rand(R,1)-0.5;m = 0:1:R-1;s = 2*m.*(0.9.m

19、);x = s + d;plot(m,d,r-,m,s,b-,m,x,g:)xlabel(Time index n); ylabel(Amplitude)legend(dn,sn,xn);pauseM = input(Number of input samples = );b = ones(M,1)/M;y = filter(b,1,x);plot(m,s,r-,m,y,b-)legend(sn,yn);xlabel (Time index n);ylabel(Amplitude)實驗二M5.1 Using MATLAB, compute the N-point DFTs the length

20、-N sequences of Problem 3.18 for N=4,6,8 and 10. Compare your result with that obtained by evaluating the DTFTs computed in Problem 3.18 at =2kN,k=0,1.,N-1.Code:N = input(The value of N = );k = -N:N;y = ones(1,2*N+1);w = 0:2*pi/255:2*pi;Y = freqz(y, 1, w);Ydft = fft(y);n = 0:1:2*N;plot(w/pi,abs(Y),n

21、*2/(2*N+1),abs(Ydft),o);xlabel(omega/pi),ylabel(Amplitude);N=4N=8N=10N=6M6.1 Using Program 6-1, determine the factored form of the following z-transforms:(a)G1=3z4-2.4z3+15.36z2+3.84z+95z4-8.5z3+17.6z2+4.7z-6 ,(b)G2=2z4+0.2z3+6.4z2+4.6z+2.45z4+z3+6.6z2+0.42z+24 .Code:% Program 6_1% Determination of

22、the Factored Form% of a Rational z-Transform%num = input(Type in the numerator coefficients = );den = input(Type in the denominator coefficients = );K = num(1)/den(1);Numfactors = factorize(num);Denfactors = factorize(den);disp(Numerator factors);disp(Numfactors);disp(Denominator factors);disp(Denfa

23、ctors);disp(Gain constant);disp(K);zplane(num,den);Figure aFigure bM8.1 Using MATLAB, develop a cascade realization of each of the following linear-phase FIR transfer function:(a)H1(z)=-0.3+0.16z-1+0.1z-2+1.2z-3+0.1z-4+0.16z-5-0.3z-6 ,(b) H2(z)=2-3.8z-1+1.5z-2-4.2z-3+1.5z-4-3.8z-5+2z-6 ,(c) H3(z)=-0

24、.3+0.16z-1+0.1z-2-0.1z-4+0.16z-5-0.3z-6 ,(d) H4(z)=-2+3.8z-1-0.15z-2+0.15z-4-3.8z-5+2z-6 ,Code: num = input(Type in the numerator coefficients = );Numfactors = factorize(num);disp(Numerator factors);disp(Numfactors);Figure aFigure bFigure cFigure dM8.2 Consider the fourth-oder IIR transfer functionG

25、(z)=0.1103-0.4413z-1+0.6619z-2-0.4413z-3+0.1103z-41-0.1510z-1+0.8042z-2+0.1618z-3+0.1872z-4 .(a)Using MATLAB, express G(z) in factored form.(b)Develop two different cascade realizations of G(z).(c)Develop two different parallel form realization of G(z).Realize each second-order section in direct fro

26、m II.Code:% Program 8_2% Factorization of a Rational IIR Transfer Function%format shortnum = input(Numerator coefficients = );den = input(Denominator coefficients = );Numfactors = factorize(num);Denfactors = factorize(den);K = num(1)/den(1);disp(Numerator Factors),disp(Numfactors)disp(Denominator Fa

27、ctors),disp(Denfactors)disp(Gain constant);disp(K);Figure a實驗三M9.1 Design a digital Butterworth lowpass filter operating at a sampling rate of 100kHz with a 0.3dB cutoff frequency at 15kHz and a minimum stopband attenuation of 45 dB at 25 kHz using the bilinear transformation method. Determine the o

28、rder of the analog filter prototype using the formula given in Eq.(A.9), and then design the analog prototype filter using the M-file buttap of MATLAB. Transform the analog filter transform function to the desired digital transfer function using the M-file bilinear. Plot the gain and phase response

29、using MATLAB. Show all step used in the design.Code:wp=2*1/4;ws=2*15/40;n1,wn1=buttord(wp,ws,3,35);B,A=butter(n1,wn1);h1,w=freqz(B,A);f=w/pi*20000;plot(f,20*log10(abs(h1),r);axis(0,20000,-80,10);grid;xlabel(Frequency/Hz);ylabel(Magnitude/dB);實驗四M10.1 Plot the magnitude response of a linear-phase FIR

30、 highpass filter by truncating the impulse response hHPn of the ideal highpass filter of Eq.(10.17) to length N=2M+1 for two different values of M, and show that the truncated filter exhibits oscillatory behavior on both sides of the cutoff frequency.Code:M=800;n= -M:M;hn= -sin(0.4*pi*n)./(pi*n);%hn= -0.4*sinc(0.4*n);hn(M+1)=0.6;H,w = freqz(hn,1);plot(n,hn)figure,plot(