How to do FT Time shift and Time scaling properties
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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.
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Wayne King
il 28 Mar 2013
Modificato: Wayne King
il 28 Mar 2013
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');
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AYDIN KARA
il 2 Gen 2021
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.
Più risposte (6)
Wayne King
il 29 Mar 2013
Modificato: Wayne King
il 29 Mar 2013
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.
Wayne King
il 28 Mar 2013
Modificato: Wayne King
il 28 Mar 2013
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.
ong
il 3 Apr 2013
1 Commento
Irfan Ali Dahani
il 19 Gen 2021
visit and you will get easy made time shifting, time scaling and amplitude scaling all in one project. surely both projects will help you.
SHREEVARSHINI R
il 24 Ott 2021
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
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Sk Group
il 25 Ott 2021
Time shifting Prove: DFT{x(n-l)} = X(K)e^(-j(2*pi/N)kl
For complete detailed post visit: https://www.swebllc.com/time-shifting-property-in-matlab-complete-prove-code-output/
1 Commento
Sk Group
il 25 Ott 2021
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/778128/image.png)
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