The person who wrote fftpack responds as follows:

Hello,

The person who wrote fftpack responds as follows:

> those terms are multiplied by 2 (4 at the corners) which is
> the standard because
> the strandard formula for the transform from Fourier to physical space
> has .5 in from of those terms, as shown in books on the subject.
> Those terms are not explicitly multiplied by 2 or 4 - rather, it occurs
> implicitly from the FFT calculation.
> I know it can seem a little strange - but only follows the standard
> established years ago....

>
> Jocelyn Rodgers wrote:
> > Hello -
> >
> > I'm really hoping someone on this list can help out. I have a
> > question regarding fftpack5, but the e-mail address contact
> listed on
> > the fftpack5 webpage is no longer valid.
> >
> > The basic issue is that I'm using the 2D real to complex forward
> > transform to analyze fluctuations in a surface. The basic
> behavior I
> > expect is that the time average of the _square_ of the fourier
> > transform should simply be a function of the magnitude of k.
> >
> > For the most part the results I obtain bear this out. Nearly all
> the
> > points lie on a single curve. However a certain subset of those
> > points only lie on that curve when multiplied by a factor of 4.
> These
> > datapoints, following the notation in the documentation for RFFT2F,
> > correspond to
> >
> > * i=0 with any j, and
> > * i=L/2 with any j.
> >
> > The high order of the points that are different made me wonder if a
> > factor of 2 was left out somewhere in fftpack5 for those edge lines
> > (leading to the factor of 4 difference in the square magnitude of
> the
> > transform).
> >
> > I appreciate anyone's time in taking a look at this. Even
> suggestions
> > of what to look for in the library code would be helpful. And
> please
> > let me know I should send you any other info.
> >
> > Thanks so much,q
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Received on Wed Nov 12 2008 - 21:14:58 MST