Shalin Mehta

Hello, Nice work. I am running into problems with MATLAB R2011b on MAC OS Lion (Java VM Version: Java 1.6.0_29-b11-402-11M3527 with Apple Inc. Java HotSpot(TM) 64-Bit Server VM mixed mode) .

When I try to execute universe.show() from the first demonstration, I encounter following error. It looks like a permission related issue, but I cannot figure out how to resolve this.
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Error using ij3d.Image3DUniverse/show
Java exception occurred:
java.lang.SecurityException: sealing violation: package javax.media.j3d is sealed
at java.net.URLClassLoader.defineClass(URLClassLoader.java:234)
at java.net.URLClassLoader.access$000(URLClassLoader.java:58)
at java.net.URLClassLoader$1.run(URLClassLoader.java:197)
at java.security.AccessController.doPrivileged(Native Method)
at java.net.URLClassLoader.findClass(URLClassLoader.java:190)
at com.mathworks.jmi.CustomURLClassLoader.findClass(ClassLoaderManager.java:754)
at java.lang.ClassLoader.loadClass(ClassLoader.java:306)
at java.lang.ClassLoader.loadClass(ClassLoader.java:247)
at java.lang.ClassLoader.defineClass1(Native Method)
at java.lang.ClassLoader.defineClassCond(ClassLoader.java:631)
at java.lang.ClassLoader.defineClass(ClassLoader.java:615)
at java.security.SecureClassLoader.defineClass(SecureClassLoader.java:141)
at java.net.URLClassLoader.defineClass(URLClassLoader.java:283)
at java.net.URLClassLoader.access$000(URLClassLoader.java:58)
at java.net.URLClassLoader$1.run(URLClassLoader.java:197)
at java.security.AccessController.doPrivileged(Native Method)
at java.net.URLClassLoader.findClass(URLClassLoader.java:190)
at com.mathworks.jmi.CustomURLClassLoader.findClass(ClassLoaderManager.java:754)
at java.lang.ClassLoader.loadClass(ClassLoader.java:306)
at java.lang.ClassLoader.loadClass(ClassLoader.java:247)
at ij3d.ImageWindow3D.<init>(ImageWindow3D.java:64)
at ij3d.Image3DUniverse.show(Image3DUniverse.java:195)

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.
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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));