Re: Fourier transform and the like


"S. Gammelmark" <gammelmark@xxxxxxxxx> wrote in message
news:1129057102.932756.106990@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hi
>
> In Fourier seris/transforms we have a way to represent certain
> functions as an infinte 'linear combination' of the functions e^(ikx),
> where k\in Z or k\in R as in the fourier transform (I think. I'm not
> entirely sure here, but isn't the Fourier transform precicely a way of
> decomposing af function into a continuous function telling me the
> amplitudes of a e^(ikx)-term where k \in R ?)
>
> This we can also use to decompose a digital signal into frequencies
> (with certain limitations).
>
> My question is - how can we (if at all) use other functions to do this
> (I'm thinking especially e^(kx) here)? As an integral transform, or as
> a way of decomposing a digital signal into amplitudes of e^(kx)
> functions?
>
> I hope the question is clear.

No it's not! At least not to me.

Anyway, you probably already know this, but if you restrict yourself to R+
(i.e. x >= 0), then you may consider the Laplace transform.

-Michael.


.

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