西安电子科技大学-数字信号处理-试卷C
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Examination Questions on “Digital Signal Processing”
(120 minutes)
1.Let x(n)={1,-2,4,6,-5,8,10}, n=-4:2; [12 points]
(a). Determine the odd part and the even part of x(n).
(b). Calculate y(n)=2x(n-2)+ x(n+1)x(n)- x(-2-n)
(c). Write a MATLAB program to generate the sequence of y(n) in (b).
2.Given sequence x(n)={4,2,1,0,1,2,4} with sample period Ts=0.001sec. [25 pints]
(a). Determine the expression X(e jω)= DTFT[x(n)], discuss the periodicity of X(e jω).
(b). Write a MATLAB program for plotting magnitude and phase response of X(e jω),
where ω is evenly separated into 1000 points between [0,π] radius. (You needn’t plot it)
(c). Guess and make comments on the property of its angle plot. Why?
(d). Determine the corresponding analog frequency of the digital frequency
ω=0.3π, and ω=1.3π.
(e). Comment on the difference of amplitude and magnitude responses.
3.Given a system described by the following difference equation: [18 points]
-
x
-
+
n
=n
n
n
y
y
n
y
x
(
+
)2
)
(
)1
(
(
(-
-
)
9.0
)1
9.0
Determine:
(a). The system function H(z) and its zero-pole plot.
(b). The region of convergence and its impulse response sequence h(n) if the given
system is a causal system.
(c). The region of convergence and its impulse response sequence h(n) if the given
system is a stable system.
pute the N-point circular convolution for the following sequences: [20 points]
(a). x 1(n )={1,2,3,4}, x 2(n )={5,6,7}, N =4; (b). Calculate the same circular convolution for N =7;
(c). Determine the minimum N when circular convolution equal to linear
convolution.
(d). Write a MATLAB program to calculate the circular convolution using the
DFT.
(e). Comments on the difference among the DTFT, the DFT and the FFT.
5. For the digital filter structures, [10 points]
(a). Please explain the advantages of the direct form II over the direct form I for the IIR filter.
(b). Please explain the advantage of the linear-phase form for the FIR filter. (c). Draw the linear-phase form of the given system function
654321253521)(------++++++=z z z z z z z H
6. Design a bandpass FIR filter using the window design technique. [10 points]
The specifications are given as follows:
lower stopband edge: 0.2π, As = 60dB lower passband edge: 0.3π, Rp = 0.5dB upper passband edge: 0.6π, Rp = 0.5dB upper stopband edge:
0.7π, As = 60dB
(a). Select the proper window function; (b). Give the main design steps;
(c). How to verify the actual ripple is indeed within the given tolerance? Please list
the corresponding MATLAB program statements.
7. Give the basic steps to design a digital highpass IIR filter from the given specifications of s p s p A R ,,,ωω. [5 points]
(END)。
