From help-octave-request at bevo dot che dot wisc dot edu Mon Dec 29 14:43:31 2003
Subject: Re: convolution and fourier transform
From: Christoph Dalitz <christoph dot dalitz at hs-niederrhein dot de>
To: Przemek Klosowski <przemek at jazz dot ncnr dot nist dot gov>
Cc: help-octave at bevo dot che dot wisc dot edu
Date: Mon, 29 Dec 2003 21:39:33 +0100

On Mon, 29 Dec 2003 15:14:17 -0500 (EST)
Przemek Klosowski <przemek at jazz dot ncnr dot nist dot gov> wrote:

>    Are there also functions (maybe in octave-forge?) which compute
>    the *continuous* convolution (\int_0^x f(x-y)g(y)dy or 
>    \int_{-\infty}^\infty f(x-y)g(y)dy) and the *continuous* fourier
>    transform of functions?
> 
> what would be the result of such operation---a function? Octave isn't 
> a symbolic algebra system, just a linear algebra/numerical tool, so
> the primitive objects are discrete matrices, not generalized functions;
> the operations on those are necessarily discretized.
> 
Both the convolution and the fourier transform are integrals with a parameter.
Thus I am looking for a function which calculates numerically these integrals
for a given set of parameters. For instance

	convolution("f","g",xvec)

would compute the convolution of the user defined functions f and g at the given
points xvec. While this could be emulated with the discrete convolution (just interpret
it as a Riemann sum), the same is not easily done with the Foruier transform: although
the Discrete Fourier Transform is somehow related to the Riemann sum of the integral Fourier
transform, numerical accuracy requires some sophisticated iteration to control the aliasing
effect.

Christoph



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