數(shù)字信號(hào)處理試卷試題及答案

數(shù)字信號(hào)處理試卷試題及答案,數(shù)字信號(hào),處理,試卷,試題,答案,謎底 Examination B on “Digital Signal Processing”1. Suppose x(n)=δ(n)+δ(n-1),Do the following: [8](a). Determine X(jω)=DTFT[x(n)],plot its amplitude and phase response.(b). Determine X(k)=DFT[x(n)] with period length N=4. Plot amplitude response |X(k)|~k.2. Given the difference equation of a discete system: y(n)=0.8y(n-1)+0.36y(n-2)+x(n)(a). Determine its system function H(z): [12](b). Suppose x(n)=(0.8)nu(n),calculate the z-transform of x(n) and y(n):X(z) and Y(z)(c). Write two MATLAB programs based on different methods to get the inverse z-transform of Y(z).3. Given the first five values of the 8-point DFT of a real-valued sequence x(n): [8]X(k)=DFT[x(n)]={0.3, 0.2+j0.5, 0 ,0.1-j0.2, 0.6,…}; k=0,1,…4,(a). Explain how to determine the sequence x(n)(n=0,1,…7) by using the properties of DFT.(b). Develop a MATLAB program to solve this problem.4. Given the system function of a filter: [8])7.0(5.90(32)???zzHPlot its: (a)direct structure form flowgraph.(b)cascade structure form flowgraph.5. Design a lowpass Butterworth analog prototype filter. The specifications are; [8]passband edge: 300Hz Rp=1dBstopband edge: 400Hz As = 50dB, (a). Give the main design steps.(b). Give the corresponding MATLAB program statement for each step.6. The MATLAB function imp_invr.m was given in the textbook: [20]function [b,a] = imp_invr(c,d,T)% Impulse Invariance Transformation from Analog to Digital Filter% ---------------------------------------------------------------[R,p,k] = residue(c,d); % statement 1p = exp(p*T); % statement 2[b,a] = residuez(R,p,k); % statement 3b = real(b'); a = real(a'); % statement 4(a). Give the analytical expressions of the impulse invariance transformation(b). Give comments to each of the four statements regarding to the analytical expressions(c). Give comments to each variables in different statements.