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Re: Convolution, IDL & Numerical Recipes [message #32675 is a reply to message #32672]

Thu, 31 October 2002 17:10

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

David Fanning wrote:
...
> Gonzales and Woods seem to suggest that "convolution" is a
> frequency domain concept, and can only be loosely applied in
> the linear spatial sense. Could this be part of the problem?

The convolution isn't specifically a frequency-domain concept. In fact,
as I'm usually seen it, the canonical definition is in the time domain.
cgh(t) is the convolution of g(t) and h(t) if:

cgh(t) = integral(g(tau)h(t-tau) d tau)

The importance of the frequency domain for convolutions is that it can
be proven that if G(f), H(f), and CGH(f) are the fourier transforms of
g(t), h(t), and cfg(t) respectively, then:

CGH(f) = G(f)*H(f)

If they'd been thinking in the frequency domain, there's no way they'd
have named it using a word that is closely related to "convoluted".

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[Message index]

		Re: Convolution, IDL & Numerical Recipes By: David Fanning on Fri, 01 November 2002 06:48
		Re: Convolution, IDL & Numerical Recipes By: R.G. Stockwell on Fri, 01 November 2002 06:09
		Re: Convolution, IDL & Numerical Recipes By: R.G. Stockwell on Fri, 01 November 2002 06:01
		Re: Convolution, IDL & Numerical Recipes By: Kenneth P. Bowman on Thu, 31 October 2002 19:41
		Re: Convolution, IDL & Numerical Recipes By: James Kuyper on Thu, 31 October 2002 17:10
		Re: Convolution, IDL & Numerical Recipes By: David Fanning on Thu, 31 October 2002 14:29
		Re: Convolution, IDL & Numerical Recipes By: JD Smith on Thu, 31 October 2002 13:48
		Re: Convolution, IDL & Numerical Recipes By: aceves on Mon, 04 November 2002 18:55
		Re: Convolution, IDL & Numerical Recipes By: David Fanning on Fri, 01 November 2002 06:53
		Re: Convolution, IDL & Numerical Recipes By: aceves on Fri, 01 November 2002 17:06

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