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From: Mat Hunt on 17 Jun 2010 15:34
I need to compute an inverse Fourier transform, I did this previously by writing my own inverse Fourier transform routine which worked pretty well on simple examples but I am currently investigating some rather obscure wave profiles.

I computed these wave profiles two ways and the answers don't agree, so I thought I would delve into the murky depths of the Matlab inverse Fourier transform.

Say for example I have a Fourier transform of the Gaussian function, which is sqrt(pi)*exp(-0.25*k.^2). What commands would I use to get back to my original Gaussian function? I looked on the help and that was of no use, it mentioned the ifft function but not how I should use it.

If I do the following for the Fourier transform k=-100:0.001:100, and the Fourier transform is sqrt(pi)*exp(-0.25*k.^2)

What commands do I use to get back the the original function? I also want to be able to plot it. The function I am using is defined analytically, would it be better to use the symbolic ifourier instead?

Mat
From: Walter Roberson on 17 Jun 2010 15:45
Mat Hunt wrote:

> If I do the following for the Fourier transform k=-100:0.001:100, and
> the Fourier transform is sqrt(pi)*exp(-0.25*k.^2)

You appear to be mixing the discrete Fourier transform and the continuous
Fourier transform. The discrete fourier routine is fft() and the inverse
discrete fourier transform is ifft(). I believe the continuous fourier
transform requires the symbolic toolbox (continuous implies infinite if done
numerically) , but perhaps it is supported in some other way as well.
From: Mat Hunt on 17 Jun 2010 17:49
I want to compute an inverse Fourier transform and plot the solution. I have the analytical expression of the inverse Fourier transform. I can either supply it as an analytical function (and use ifourier) or give it as a numerical array and use ifft.

Which would be best?

Mat
From: Walter Roberson on 17 Jun 2010 17:58
Mat Hunt wrote:
> I want to compute an inverse Fourier transform and plot the solution. I
> have the analytical expression of the inverse Fourier transform. I can
> either supply it as an analytical function (and use ifourier) or give it
> as a numerical array and use ifft.
>
> Which would be best?

I would try ifourier first as it would be more accurate -- using the discrete
fourier is going to give you round-off problems.

If your function is sufficiently complex then there might not be a nice
symbolic inverse transform; in that case you would have to resort to ifft.
From: Mat Hunt on 17 Jun 2010 18:29
Walter Roberson <roberson(a)hushmail.com> wrote in message <hve5un$mj1$1(a)canopus.cc.umanitoba.ca>...
> Mat Hunt wrote:
> > I want to compute an inverse Fourier transform and plot the solution. I
> > have the analytical expression of the inverse Fourier transform. I can
> > either supply it as an analytical function (and use ifourier) or give it
> > as a numerical array and use ifft.
> >
> > Which would be best?
>
> I would try ifourier first as it would be more accurate -- using the discrete
> fourier is going to give you round-off problems.
>
> If your function is sufficiently complex then there might not be a nice
> symbolic inverse transform; in that case you would have to resort to ifft.

The function in question is:

16.2668*exp(-1/4*k^2)/(144+2*k^4-12*k^2+9*abs(k))

I tried ifourier and I got the result:

16.2668*ifourier(exp(-1/4*k^2)/(144+2*k^4-12*k^2+9*abs(k)),k,x)

So I think I will have to use ifft. I would ideally like to plot the original function but I don't know how to plot it.

Mat
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