How to do FT Time shift and Time scaling properties

조회 수: 96 (최근 30일)
ong
ong 2013년 3월 28일
댓글: Peter Seibold 2022년 8월 29일
Currently i am trying use matlab to do the FT properties -time shift and time scaling, can someone help me in the implementation? i would like to prove that Timeshift: F[x(t-τ) ]= e^(-jwτ) F[x(t)]
Time scaling: F[x(at)]=1/(|a|) X(w/a)
Thanks.

채택된 답변

Wayne King
Wayne King 2013년 3월 28일
편집: Wayne King 2013년 3월 28일
t=0:0.001:0.1-0.001;
Fs = 1e3;
freq1 = 100;
x1=cos(2*pi*freq1*t);
Delay=2;
yp = fft(x1);
yp = yp(1:length(x1)/2+1);
f = 0:Fs/length(x1):500;
yp = yp.*exp(-1i*2*pi*f*Delay*(1/Fs));
yp = [yp conj(fliplr(yp(2:end-1)))];
y = ifft(yp,'symmetric');
plot(t(1:100),x1(1:100),'b');
hold on;
plot(t(1:100),y(1:100),'r');
  댓글 수: 2
ong
ong 2013년 3월 29일
Hi Wayne, thanks for your help. I am able to observe the shift but i couldn't get the same plot result when comparing:
D=2;
Fs=1000;
freq1=100;
t=0:0.001:1-0.001;
x=cos(2*pi*freq1*(t-D));
y1 = fft(x);
and
x1=cos(2*pi*freq1*t);
Delay=2;
yp = fft(x1);
yp = yp(1:length(x1)/2+1);
f = 0:Fs/length(x1):500;
yp = yp.*exp(-1i*2*pi*f*Delay*(1/Fs));
any reason why? Thanks.
AYDIN KARA
AYDIN KARA 2021년 1월 2일
Your code just fails when sampling frequency increases.
For f = 1e4 it gives matrix dimensions must match error. Other wise if I keep your sampling frequency at 1e6
After that point, even if I increase the delay by 2000. I could not observe any delay.
Sorry but it seems your code works for one case.

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추가 답변 (6개)

Wayne King
Wayne King 2013년 3월 29일
편집: Wayne King 2013년 3월 29일
They agree if you get the delay right. You're not delaying the signal by 2. You're trying to delay the signal by two samples, but that has to take into account the sampling interval, so you're actually delaying the signal by 0.002 seconds.
t = 0:0.001:1-0.001;
freq1 = 100;
Fs = 1000;
x1=cos(2*pi*freq1*t);
Delay=2;
yp = fft(x1);
yp = yp(1:length(x1)/2+1);
f = 0:Fs/length(x1):500;
yp = yp.*exp(-1i*2*pi*f*Delay*(1/Fs));
yp = [yp conj(fliplr(yp(2:end-1)))];
yrec = ifft(yp,'symmetric');
Compare with
D=2;
Fs=1000;
freq1=100;
t=0:0.001:1-0.001;
x=cos(2*pi*freq1*(t-(D*(1/Fs))));
y1 = fft(x);
y1T = ifft(y1,'symmetric');
max(abs(y1T-yrec))
You can see the above are identical. Thank you for accepting my answer if I have helped you.
  댓글 수: 1
ong
ong 2013년 3월 29일
Hi there, Thanks for the clear explanation. However, i have one more issue, does it work the same way if i m having my fft display in the angle instead of abs?
I tried having it plot in the phase domain but there is some differ in the result.

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Wayne King
Wayne King 2013년 3월 28일
편집: Wayne King 2013년 3월 28일
n = 0:159;
x = cos(pi/4*n);
y = cos(pi/4*(n-2));
xdft = fft(x);
ydft = fft(y);
xdft(21)
ydft(21)
Note that 80+i0 has become 0-80i due to the predicted phase shift of e^{-i\pi/2}
Obviously, the only way to properly "prove" that theorem is mathematically.
The scaling one you have to be careful with in discrete-time because scaling doesn't work the same with a discrete variable as it does with continuous time.
  댓글 수: 1
ong
ong 2013년 3월 28일
Is there anyway that i can do it in this form:
t=0:0.001:1
x1=cos(2*pi*freq1*t)
Delay=2
yp = fft(x1);
yp = yp.*exp(-j*2*pi*t*Delay);

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ong
ong 2013년 4월 3일
To update on this question, Wayne King provided the explanation and the steps provided are accurate. However there is one problem, instead of ifft the abs function, it was to display in the phase domain, here, the phase for the time shift properties and the function:cos(2*pi*freq1*(t-(D*(1/Fs) doesnt match.
There are error to the phase shift, anyone can help please?
Thanks.
  댓글 수: 1
Irfan Ali Dahani
Irfan Ali Dahani 2021년 1월 19일
visit and you will get easy made time shifting, time scaling and amplitude scaling all in one project. surely both projects will help you.

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SHREEVARSHINI R
SHREEVARSHINI R 2021년 10월 24일
1.Write a MATLAB program to find Fourier transform of the signal Ate-btu(t)
2.Write a MATLAB program to perform amplitude scaling, time scaling and time shift on the signal x(t) = 1+t; for t=0 to 2

Sk Group
Sk Group 2021년 10월 25일
  댓글 수: 1
Peter Seibold
Peter Seibold 2022년 8월 29일
Proposed code NOT working! Unknown function 'sigshift1'.

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Sk Group
Sk Group 2021년 10월 25일

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