Re: inverse fourier transform

[Heber Farnsworth]

Something seems wrong about this.  Why does the function need to be 
symmetric for ifft to give a real answer?  On some level this makes 
sense because I know that even functions have real transforms.  But I 
know this function is not even (for those with experience in statistics 
I have a distribution which is skewed).  But the distribution is real.  
Why can't I do an inverse transform to recover the distribution from 
it's fourier transform?

I looked more closely at the fourier transform which I'm trying to 
invert.  I call it phi.

plot(real(fftshift(phi)))

It's real part is symmetric (even)

plot(imag(fftshift(phi)))

and it's imaginary part is odd (looks just like sin on [-pi:pi])

Heber

On Wednesday, April 2, 2003, at 01:07 AM, Quentin H. Spencer wrote:

> Heber Farnsworth wrote:
>
> > Some of you will laugh at me for this but I've never done an inverse 
> > fourier transform.  I need to use a probability density function 
> > which I don't know in closed form but I do have a closed form for 
> > it's characteristic function (fourier transform).  But when I try 
> > ifft I get something that is complex.  I know that this thing is the 
> > fourier transform of a real density.  How do I get a real (not 
> > complex) thing out of this?  Here some things I'm not sure about 
> > which may be causing my confusion.
> >
> > 1.  I'm not sure what range of frequencies to use:  [-pi,pi]? 
> > something else?
> >
> > 2.  I may not be using fftshift correctly.
>
> This is possible. Misalignment by one sample is enough to cause
> problems. You do want to choose frequencies from [-pi,pi], and assuming
> you want real output, you need the function to be symmetric around 0. 
> If
> you are doing, say, a 64 point IFFT, index 1 is DC, and index 33 is
> Nyquist (pi and -pi), so indices [2:32] must be a mirror image of
> indices [34:64] in order for the IFFT to be real. Because of machine
> precision, you will always get complex output, so after you verify that
> the imaginary part is just noise, you can ignore it.
>
> > Is there anyone out there that does this a lot that can give me some 
> > pointers?
> >
> > Heber Farnsworth



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