數(shù)字信號處理試卷試題及答案

數(shù)字信號處理試卷試題及答案,數(shù)字信號,處理,試卷,試題,答案,謎底 Digital Signal Processing of 20051Answer to “Digital Signal Processing of 2005”Problem 1(a) even part: odd part: ;5.0,17,15.0eX ;5.0,13,5.0oX(b) 26943,62,y(c) MATLAB Programn=-4:2;x=1 -2 4 6 -5 8 10;x11,n11=sigshift(x,n,2);x12,n12=sigshift(x,n,-1);x13,n13=sigfold(x,n);x13,n13=sigshift(x13,n13,-2);x12,n12=sigmult(x,n,x12,n12);y,n=sigadd(2*x11,n11,x12,n12);y,n=sigadd(y,n,-1*x13,n13)Problem 2(a) ， is periodic in with period 2wjjwjwjjjw eeeeX 6542 42104)( ()jX(b) MATLAB Program:clear; close all;n = 0:6; x = 4,2,1,0,1,2,4;w = 0:1:1000*pi/1000;X = x*exp(-j*n*w); magX = abs(X); phaX = angle(X);% Magnitude Response Plotsubplot(2,1,1); plot(w/pi,magX);grid;xlabel(frequency in pi units); ylabel(|X|);title(Magnitude Response);% Phase response plotsubplot(2,1,2); plot(w/pi,phaX*180/pi);grid;xlabel(frequency in pi units); ylabel(Degrees);title(Phase Response); axis(0,1,-180,180) (c) Because the given sequence x (n)=4,2,1,0,1,2,4 (n=0,1,2,3,4,5,6) is symmetric about ,the 132Nphase response satisfied the condition：()jHe()3jHeso the phase response is a linear function in . (d) ;150,350zz(e) The difference of amplitude and magnitude response:Digital Signal Processing of 20052Firstly, the amplitude response is a real function, and it may be both positive and negative. The magnitude response is always positive. Secondly, the phase response associated with the magnitude response is a discontinuous function. While the associated with the amplitude is a continuous linear function. Problem 3(a) )9.0.1/()() 21zzHZero:0 and 1;Pole:-0.6 and 1.5;(b) ， 11165()220Hzzz165()(0.)(1.)(22nnhnu(c) ROC : ， .6.5Z633251n nhnuProblem 4(a) y(n)=50,44,34,52;(b) y(n)=5,16,34,52,45,28,0;(c) N=6;(d) MATLAB Program:Function y=circonv(x1,x2,N)If (length(x1)N)error(“N must not be smaller than the length of sequence”)elsex1=x1,zeros(1,N-length(x1);endif(length(x2)N)error(“N must not be smaller than the length of sequence”)Digital Signal Processing of 20053elsex2=x2,zeros(1,N-length(x2); endy1=dft(x1,N).*dft(x2,N);y=idft(y,N);(e) DTFT is discrete in time domain, but continuous in frequency domain. The DFT is discrete both in time and frequency domain.The FFT is a very efficient method for calculating DFT. Problem 5(a) Direct form II uses the little delay and it can decrease the space of the compute.(b)The advantage of the linear-phase form:1. For frequency-selective filters, linear-phase structure is generally desirable to have a phase-response that is a linear function of frequency. 2. This structure requires 50% fewer multiplications than the direct form.(c) Block diagrams are shown as under:1z 1z 1z 1z 1z 1z1253521()xn ()yn()xn()yn 1z 1z 1z1z1z1z1 2 5 3Problem 6(a) we use Hamming or Blackman window to design the bandpass filter because it can provide us attenuation exceed 60dB .(b) According to Blackman window :first, Determine transition width = ;psWsecond, Determine the type of the window according to ;sAthird, Compute M using the formula ;Mps2fourth, Compute ideal LPF ;scfifth, design the window needed, multiply point by point;sixth, determine spAR,(c) MATLAB Program:Digital Signal Processing of 20054% Specifications about Blackman window:ws1 = 0.2*pi; % lower stopband edgewp1 = 0.3*pi; % lower passband edgewp2 = 0.6*pi; % upper passband edgews2 = 0.7*pi; % upper stopband edgeRp = 0.5; % passband rippleAs = 60; % stopband attenuation%tr_width = min(wp1-ws1),(ws2-wp2);M = ceil(6.6*pi/tr_width); M = 2*floor(M/2)+1, % choose odd Mn = 0:M-1;w_ham = (hamming(M);wc1 = (ws1+wp1)/2; wc2 = (ws2+wp2)/2;hd = ideal_lp(wc2,M)-ideal_lp(wc1,M);h = hd .* w_ham;db,mag,pha,grd,w = freqz_m(h,1);delta_w = pi/500;Asd = floor(-max(db(1:floor(ws1/delta_w)+1), % Actual AttnRpd = -min(db(ceil(wp1/delta_w)+1:floor(wp2/delta_w)+1), % Actual passband ripple （5）% Filter Response Plotssubplot(2,2,1); stem(n,hd); title(Ideal Impulse Response: Bandpass);axis(-1,M,min(hd)-0.1,max(hd)+0.1); xlabel(n); ylabel(hd(n)set(gca,XTickMode,manual,XTick,0;M-1,fontsize,10)subplot(2,2,2); stem(n,w_ham); title(Hamming Window);axis(-1,M,-0.1,1.1); xlabel(n); ylabel(w_ham(n)set(gca,XTickMode,manual,XTick,0;M-1,fontsize,10)set(gca,YTickMode,manual,YTick,0;1,fontsize,10)subplot(2,2,3); stem(n,h); title(Actual Impulse Response: Bandpass);axis(-1,M,min(hd)-0.1,max(hd)+0.1); xlabel(n); ylabel(h(n)set(gca,XTickMode,manual,XTick,0;M-1,fontsize,10)subplot(2,2,4); plot(w/pi,db); title(Magnitude Response in dB);axis(0,1,-As-30,5); xlabel(frequency in pi units); ylabel(Decibels)set(gca,XTickMode,manual,XTick,0;0.3;0.4;0.5;0.6;1)set(gca,XTickLabelMode,manual,XTickLabels,0;0.3;0.4;0.5;0.6;1,.fontsize,10)set(gca,TickMode,manual,YTick,-50;0)set(gca,YTickLabelMode,manual,YTickLabels,-50;0);gridProblem 7Firstly, we use the given specifications of to design an analog lowpass IIR filter. spsAR,Secondly, we change the analog lowpass IIR filter into the analog highpass IIR filter. Thirdly, we change the analog highpass IIR filter into the digital highpass IIR filter.