数字信号处理(双语)

安徽大学2015—2016学年第 2 学期 《数字信号处理》考查试卷（A 卷）

（开卷 时间120分钟）

院/系 年级 专业 姓名 学号

一、简答题（每小题5分，共20分）

1. Please translate the following passage into Chinese

Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, control of

systems, biomedical signal processing, seismic data processing, among others. DSP algorithms have long been run on standard computers, as well as on specialized processors called digital signal processors, and on purpose-built hardware such as application-specific integrated circuit (ASICs). Currently, there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors, among others.

2. Please describe Sampling Theorem.

3. Please give the calculation steps of FFT-based fast linear convolution algorithm.

4.Please list the platforms for DSP Implementation, and discuss the benefits and drawbacks of each implementation

二、计算题（每小题10分，共40分）

1. An FIR filter is described by the I/O equation:

1

()[()2(2)(4)]4

y n x n x n x n =--+-

Determine its transfer function H (z) and impulse response h (n )

2. Calculate the convolution of the following filter and input signals.

h =[1,0, -1], x =[1, 1,0,1,1]

3. Compute the z-transform of the following sequences and determine the corresponding region of convergence.

(1)()2cos()()4

n x n n u n π

-=

(2) ()()2()n x n u n u n =--

4. Compute the DFT of the following sequences:

(1) x1[n]={1,0,1};

(2) x2[n]=u(n)-u(n-5)

三、综合题（每小题20分，共40分）

1. Using z-transform, determine the transfer function H(z) and from it the casual impulse response h(n) of the linear system described by following I/O difference equations; (20)

y(n)-0.5y(n-1)=x(n);

Determine also the frequency response H(ω), the pole/zero pattern of the transfer function on the z-plane, draw a

rough sketch of the magnitude response |H((ω)| over the right half of Nyquist interval 0≤ω≤π,

2.A digital speech signal was corrupted by the power-line interference (50Hz), which could be removed by a temporal filter. Assuming the digital speech signal is saved in a data file called 'speech.wav', please give the matlab codes to implement the following tasks:

(1) filter designing and power-line interference removing

(2) Spectrum calculation for original and corrected speech signals.

(3) Draw the waveforms of time signals and the corresponding magnitude spectrums