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From: Fatemeh on 23 Jun 2008 03:07
I'm looking for a subroutine of Fortran90 about "Fast Fourier
Transform of a Step-function in 3-dimonsional."
I read the related subroutines in Numerical Recipes Book, but I
couldn't match it for a 3D step function.
Whould you please let me to have access to a subroutine for mentioned
goal? I don't know how I should match this subroutine between 3D step
function and FFT.

I'm anxiously looking forward your reply.

Kind Regards,
Fatemeh
From: glen herrmannsfeldt on 23 Jun 2008 05:26
Fatemeh wrote:

> I'm looking for a subroutine of Fortran90 about "Fast Fourier
> Transform of a Step-function in 3-dimonsional."
> I read the related subroutines in Numerical Recipes Book, but I
> couldn't match it for a 3D step function.
> Whould you please let me to have access to a subroutine for mentioned
> goal? I don't know how I should match this subroutine between 3D step
> function and FFT.

The Fourier transform is separable in rectangular coordinates.

Does that help?

-- glen

From: Damian on 24 Jun 2008 03:50
On Jun 23, 2:26 am, glen herrmannsfeldt <g...(a)ugcs.caltech.edu> wrote:
> Fatemeh wrote:
> > I'm looking for a subroutine of Fortran90 about "Fast Fourier
> > Transform of a Step-function in 3-dimonsional."
> > I read the related subroutines in Numerical Recipes Book, but I
> > couldn't match it for a 3D step function.
> > Whould you please let me to have access to a subroutine for mentioned
> > goal? I don't know how I should match this subroutine between 3D step
> > function and FFT.
>
> The Fourier transform is separable in rectangular coordinates.
>
> Does that help?
>
> -- glen

This is more a question for a numerical analysis newsgroup such as
sci.math.num-analysis since it's not Fortran-specific. (In fact, the
latest edition of Numerical Recipes abandons Fortran altogether in
favor of C++).

Nonetheless, the short answer is that the appropriate Numerical
Recipes Fortran 90 procedure is called "realft3" assuming your initial
data is real.

What is your intended application? If it is only to compute the FFT
of step functions, that seems strange for at least two reasons:
(1) the FFT of a step function in 1D can be written down by inspection
and the transform of a 3D step function is separable into products of
1D step functions at least in rectangular coordinates as noted by the
previous response to your post so it's not clear why you would want to
compute it, and
(2) step functions are discontinuous and aperiodic, so they are not
well represented by Fourier transforms (particularly if one is
interested in differentiating or interpolating the resulting series)
unless you're planning to use windowing.

Also, if you're working in 3D, there is a good chance you're working
with large enough data sets for runtime performance to be important.
While Numerical Recipes emphasizes clarity for instructive purposes,
even the authors point out that other implementations tuned for
specific hardware will invariably outperform their routines. Some of
faster alternatives are freely available, e.g. FFTW (http://
www.fftw.org).

Damian

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