信号与系统-期末考试试卷2009B-(1)

一、 选择题（4分/每题，共20分）1. Determine the output of the systems described by following differential equation: ，Determine zero-initial response and zero-state response ：（ ）（A）,，（B）,（C）,（D）,2. Evaluate the following discrete-time convolution sums: = ( )(A) (B) (C) (D) 3. The FS ofis , the FS of ( ) is .(A) (B) (C) (D) 4. The frequency response of a LTI system is , it is distortionless transmission or not? Determine the system output if the input is x(t)=sint+sin3t (-t) . ( )(A) it is distortionless transmission; (B) it is not distortionless transmission; (C) it is distortionless transmission; (D) it is not distortionless transmission; 5. The impulse response of a LTI system is ,the step response for the system is ( )(A) (B), here (C) (D) , here 二、 填空题（4分/每题，共20分）1. A system has inputand output . If the system has properties, then the input and output pairs has the relationship: input is, so output is 。2. Consider sampling ，determine the maximum of sampling interval T so that there will be no aliasing, (s).3. Write or Sketch the spectrum of Rectangular pulse xn: There is the inverse relationship between the time and frequency extent of a signal, and the Time-Bandwidth Product of xn is 4. the impulse response of integrator is ，the impulse response of differentiator is , the impulse response of discrete-time time-shift operator is 。5. write the advantages of modulation application to communication systems:(1) (2) (3) (4) 三、 计算题（共60分）1. （12 scores）A signal is shown below: 1）Determine the Fourier Transform for the signals ;2) sketch ;3) Determine .2. （10 scores） A continuous-time periodic signal 1） determine the FS coefficients ，sketch the magnitude and phase spectra;2） If pass a LTI system which has frequency response , determine and sketch its spectra.3. （12 scores） A causal LTI system described by the differential equation： yn - 3/4 yn -1 +1/8yn -2 = xn +1/5xn -11） Draw direct form II implementations of the LTI system；2） Determine the transfer function H(Z) and the impulse response hn;3） Is the system stable?4. （13 scores）Consider the system depicted in (a) below. The FT of the input signal is depicted in (b).Let and .Sketch and for the following cases: and .5. （13 scores）Discrete-time processing of continuous-time signals is shown below. Here , ，the time wave and spec