西安电子科技大学-数字信号处理-试卷A

Examination A on “Digital Signal Processing”

1. Let x(n)={3,7,-2,-1,5,-8},n=0:5; [7] (a). Determine the sequences x1(n)=x(n+2) and x2(n)=x(n-1)

(b). calculate y(n)=2x(n+2)+x(n-1)

(c). Write a MATLAB program to generate the sequence of (b).

2. Given sequence x(n)={4,3,2,0,2,3,4} with sample period Ts=0.1sec. [15]

(a). Determine the expression X(e j ω)= DTFT[x(n)], discuss the periodicity of X(e j ω).

(b). Write a MATLAB program for plotting magnitude and angle response of X(e j ω), where ω

is evenly separated into 100 points between [0,π] radius. (You needn’t plot it)

(c). Guess and make comments on the property of its angle plot.

(d). Comment on the difference of amplitude and magnitude response. Give the function name in the textbook that can determine the amplitude response.

3. Given the system function of a stable discrete system in z-transform: [12]

H(z)= (1+z -1)/(1+0.5 z -1-0.24z -2)

Determine: (a). Its zero-pole plot.

(b). Its difference equation representation.

(c). Its impulse response sequence h(n) using partial fraction representation, give the first 5 points.

(d). Give two MATLAB statements that can calculate the first 5 points of

impulse response.

4. Compute the N-point circular convolution for the following sequences: [10]

(a). x 1(n)={1,-1,1,-1}, x 2(n)={2,1,1,2}, N=4;

(b)..Calculate the same circular convolution for N=8;

(c) Determine the minimum N when circular convolution equal to linear convolution (d). Write a MATLAB program to calculate the circular convolution using DFT.

5. A linear time-invariant system is given by the function: [8]

654321253521)(------++++++=z z z z z z z H

(a). Draw the flowgraph of the direct structure form. (b). Draw the flowgraph of the linear-phase form, explain its advantage.

6. Design a bandpass FIR filter using the window design technique.

[15] The specifications are;

lower stopband edge: 0.2π upper stopband edge: 0.6π

lower passband edge: 0.3π upper passband edge: 0.5π

As = 50dB, Rp=0.5dB

(a). Select the proper window function;

(b). Give the main design steps and

(c). List the corresponding MATLAB program statements.