MATLAB机考样题(带答案)

MATLAB 机考样题：

（1）Generate and plot sequence

121[]2cos() [][4]8x n n and x n x n π

==-, with 20n 20-≤≤.

n1=-20:20;

x1=2*cos(pi/8*n1);

n2=n1-4;

x2=2*cos(pi/8*n2);

subplot(2,1,1);

plot(n1,x1);

subplot(212);

plot(n2,x2); （2）Write a MATLAB program to compute and plot the impulse response of a causal finite-dimensional discrete-time system characterized by a difference equation of the following form:

3]

-x[n 86.0 2]-1.32x[n 1]-0.34x[n x[n]8.13]-0.72y[n -2]-0.5y[n 1]-0.3y[n y[n]--+=++N=input('请输入你要求的点数N=');

num=[1.8 0.34 -1.32 -0.86];

den=[1 0.3 0.5 -0.72]; x=[1 zeros(1,N-1)];（单位冲击）

y=filter(num,den,x);

plot(0:N-1,y);

（3）Write a MATLAB program to compute and display the poles and zeros , to compute and display the second-order factored form , and to generate the pole-zero plot of a z-transform that is a ratio of two polynomials in z -1. Using this program to analyze the following G(z):

3213

211768.018.052.115.1082.2393.61.8)(-------+++-+=z z z z z z z H

num=[8.1 6.93 -23.82 10.5];

den=[1 1.52 0.18 -0.1768];

sos=tf2sos(num,den) %tf2sos 表示为1/z 的升幂

zplane(num,den)

（4）Try to give a program to evaluate the following DTFT in the range πω≤≤0 :

ωωωωω

ωωω4324321245535952)(j j j j j j j j e e e e e e e e z G --------++++++++=

%由于用freqz 计算频点至少是2个，所以至少输入两个频点

w1=input('请输入你要计算的频点w1=');

w2=input('请输入你要计算的频点w2=');

w=[w1 w2];

num=[2 5 9 5 3];

den=[5 45 2 1 1];

h=freqz(num,den,w)

（6）Write a MATLAB program to compute and plot the magnitude response of a causal LTI discrete-time system with a transfer function given by

2

127.05.01)1(15.0)(---+--=z z z z H

num=0.15*[1 0 -1];

den=[1 -0.5 0.7];

[h,w]=freqz(num,den,512);

plot(w/pi,abs(h)); （7）Consider the following FIR transfer function:

123456

()10.60.490.480.140.120.09H z z z z z z z ------=++---+

Using MATLAB to determine its zero locations and plot its magnitude and phase response.

h=[1 0.6 .49 -0.48 -0.14 -0.12 0.09];

figure(1)

zplane(h,1);

[H,w]=freqz(h,1,512);

figure(2)

plot(w/pi,abs(H));

figure(3)

plot(w/pi,angle(H));

（8）Given a signal ()4cos0.1x t t t π=+, when using a sampling frequency f T = 20KHz, plot the magnitude and phase spectrum of the sampled sequence(given length-64).

fs=2e4;

n=0:63;

x=4*n/fs+cos(0.1*pi*n/fs);

h=fft(x,1024);

figure(1);

plot(0:2/1023:2,abs(h));

figure(2);

plot(0:2/1023:2,angle(h));

（9）design an IIR butterworth digital lowpass filter with the following specifications: sampling rate of 40kHz, passband edge frequency of 4kHz, stopband edge frequency of 8kHz, passband ripple of 0.5dB, and a minimum stopband