To Mehta, yes you r right. ifftshift is used for sequence with odd length. Thank you for the correction!
01 Mar 2010
errorbarxy
Errorbarxy allows the user to plot both horizontal and vertical errorbars.
Author: James Rooney
There is a small bug. When I display legend, the original curve and errorbar are two different items. In Matlab errorbar() function, they are one curve. Hope you can modify it
You're welcome. ifftshift is the same as fftshift for even length sequence, but different for odd length. So if one uses fftshift(fft(ifftshift(...))) things work well. By the way, scaling by dt and df to correct for scaling introduced by FFT algorithm is neat trick.
There is a problem with above recipe. It fails when you have sequence of odd length. Correct recipe is:
fftshift(fft(ifftshift(sig))) or fftshift(ifft(ifftshift(spectrum))).
A description of this can be found on my submission on fftshift, ifftshift.
To observe that above is true, run the following code with fftshift and ifftshift on inner call for computing Xfinal.
-------------------------
Bx = 50;
A = sqrt(log(2))/(2*pi*Bx);
fs = 500; %sampling frequency
dt = 1/fs; %time step
T=1; %total time window
t = -T/2:dt:T/2; %time grids
df = 1/T; %freq step
Fmax = 1/2/dt; %freq window
f=-Fmax:df:Fmax; %freq grids, not used in our examples, could be used by plot(f, X)
x = exp(-t.^2/(2*A^2));
Xan = A*sqrt(2*pi)*exp(-2*pi^2*f.^2*A^2); %X(f), analytical Fourier transform of x(t), real
Xfft = dt * fft(x); %directly using fft()
Xfftshift = dt * fft(fftshift(x)); %using fftshift() before fft()
Xfinal = dt * fftshift(fft(ifftshift(x))); %identical with analytical X(f), also note dt
subplot(211); plot(f,Xan,f,real(Xfinal),'--');
subplot(212); plot(f,imag(Xfinal));
You're welcome. ifftshift is the same as fftshift for even length sequence, but different for odd length. So if one uses fftshift(fft(ifftshift(...))) things work well. By the way, scaling by dt and df to correct for scaling introduced by FFT algorithm is neat trick.
There is a problem with above recipe. It fails when you have sequence of odd length. Correct recipe is:
fftshift(fft(ifftshift(sig))) or fftshift(ifft(ifftshift(spectrum))).
A description of this can be found on my submission on fftshift, ifftshift.
To observe that above is true, run the following code with fftshift and ifftshift on inner call for computing Xfinal.
-------------------------
Bx = 50;
A = sqrt(log(2))/(2*pi*Bx);
fs = 500; %sampling frequency
dt = 1/fs; %time step
T=1; %total time window
t = -T/2:dt:T/2; %time grids
df = 1/T; %freq step
Fmax = 1/2/dt; %freq window
f=-Fmax:df:Fmax; %freq grids, not used in our examples, could be used by plot(f, X)
x = exp(-t.^2/(2*A^2));
Xan = A*sqrt(2*pi)*exp(-2*pi^2*f.^2*A^2); %X(f), analytical Fourier transform of x(t), real
Xfft = dt * fft(x); %directly using fft()
Xfftshift = dt * fft(fftshift(x)); %using fftshift() before fft()
Xfinal = dt * fftshift(fft(ifftshift(x))); %identical with analytical X(f), also note dt
subplot(211); plot(f,Xan,f,real(Xfinal),'--');
subplot(212); plot(f,imag(Xfinal));
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