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LAB6: Investigation of Aliasing Effects
1. Exercise 1:
thy c tc ng chng ph ca tn hiu cos ti tn s 1Khz to ra mt phin
bntrn ph, di ph v gii hn mu ca tn hiu.
1.1V mt tn hiu cosin ti tn s 1Khz t nht 20 chu k. Kch cbc (chu k
lymu) l 1/10Khz.Nh vy y l tn hiu trn mu. Dng lnh soundsc chy tnhiu
ny.
Code
fs = 10000;f = 1000;
t =-0.01:1/fs:0.01;% the more samples, the longer the sound% t
=-0.9:1/fs:0.9; % about 18,000 samplesy =
cos(2*pi*f*t);plot(t,y);soundsc(y,fs);
Hnh vthu c
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S mu cn to ra m thanh t nht l 2 giy nu kch thc bc l 1/10kHz
fs=10Khz => Ts=0.0001s => s mu cn l
= 20000 mu
1.2 V mt tn hiu vi tn s ly mu theo nh l Nyquist.
Code
f = 1000;fs = 2*f;t =-0.01:1/fs:0.01;y =
cos(2*pi*f*t);plot(t,y);soundsc(y,fs);
Hnh vthu c
Tn hiu thu c nghe ging vi phin bn tn hiu trn mu.
1.3. V mt tn hiu vi tn s ly mu nhhn tn s ly mu theo nh l
Nyquist
Code
f = 1000;
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fs = 1.5*f;t =-0.01:1/fs:0.01 ;
y = cos(2*pi*f*t);plot(t,y);soundsc(y,fs);
Hnh vthu c
Tn hiu m thanh nghe nhhn so vi hai tn hiu m thanh trc.
1.4. Dng lnh plot v 3 tn hiu trn cng mt hnh v.
Code
fs1 = 10000;f1 = 1000;
t1 =-0.01:1/fs1:0.01;y1 = cos(2*pi*f1*t1);
f2 = 1000;fs2 = 2*f2;t2 =-0.01:1/fs2:0.01;y2 =
cos(2*pi*f2*t2);
f3 = 1000;
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fs3 = 3*f3/2;t3 =-0.01:1/fs3:0.01;y3 = cos(2*pi*f3*t3);
subplot(3,1,1); plot(t1,y1);subplot(3,1,2); plot(t2,y2);
subplot(3,1,3); plot(t3,y3);grid on;
Hnh vthu c
2. Exercise 2:
Trong bi ny, ta to ra mt tm hnh v bnh xe b v lm cho n quay vi tc
khcnhau ca khung (frame). B phim v bnh xe b quay l tn hiu trong min
thi gian.
Nu mt tm hnh quay tn s 10Hz ( 10 vng trn 1 giy) th tn s ly mu
Nyquistcn trnh chng ph l 2*10=20 Hz.
Tiu chun ca phim l 24 hnh trn giy. Tn s cao nht ca chuyn ng khi
ti to lim trnh chng ph l 24/2= 12Hz.
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To 3 b phim v 3 phin bn trn mu ( theo chiu kim ng h), di mu (
ngcchiu kim ng h), theo nh l Nyquist. Trong mi trng hp quay ca bnh
xe ti tc ging nhau v chthay i tc ca khung trong lnh movie2avi.
Mi frame quay 360 vi tc 24 frame trn giy th mt 360/24=15 s c
1frame. Vi thi gian 3 giy th s frame l 3*24=72 frame.
Vit mt hm matlab c tn l wheel.m to ra mt b phim biu din hnh nh
spokesquay cng chiu kim ng h ti tc khng i.
Code
function [ output ] = wheel(picture, speed, FPS)%UNTITLED2
Summary of this function goes here% Detailed explanation goes
heretheta = 0;
degPerFrame = -speed*360/FPS;for i = 1:FPS*3 % the length of the
video is 3s% rotate the imageimage = imrotate(picture, theta,
'bilinear', 'crop');% display the imageimshow(image);pause(0.01) %
allow time for the plot to drawmyMovie(i) = getframe(gcf); %
capture the frametheta = theta + degPerFrame; % calculate the angle
for the next frameendoutput = myMovie;end
Da vo hm wheel.m, ta to ra 3 bphim nh sau:
Wheel-oversample.avi
picture = imread('spokes.tif');matlabMovie = wheel(picture, 10 ,
24);movie2avi(matlabMovie, 'wheel-oversampled.avi');
Wheel-undersample.avi
picture = imread('spokes.tif');matlabMovie = wheel(picture, 20,
24);movie2avi(matlabMovie, 'wheel-undersampled.avi');
Wheel-critsample.avi
picture = imread('spokes.tif');matlabMovie = wheel(picture, 12 ,
24);movie2avi(matlabMovie, 'wheel-criticallysampled.avi');
