Re: Filterquestion
- To: mathgroup at smc.vnet.net
- Subject: [mg47636] Re: Filterquestion
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Mon, 19 Apr 2004 04:33:06 -0400 (EDT)
- Organization: The University of Western Australia
- References: <c5ob2l$1gn$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <c5ob2l$1gn$1 at smc.vnet.net>, "bamse" <bamse at kyllingen.dkkkk>
wrote:
> I am wondering if it is possible to design a filter with the impulseresponse
> h(t) such that the convolution of
> a signal p(t)=f(t)*cos(w*t)+g(t)*sin(w*t) with h(t) is equal to
> f(t)*sin(w*t)+g(t)*cos(w*t)???
>
> In other words, I am looking for a filter H(s) in the s-domain that has the
> following property:
>
> InverseLaplace { H(s)*P(s) } = f(t)*sin(w*t)+g(t)*cos(w*t)
>
> where P(s)=Laplace{p(t)}
>
> Some more info:
>
> f(t) is a train of half-sine pulses with the period T
>
> g(t) is also a train of half-sine pulses with the period T, but
> g(t) is delayed 0.5T in relation to f(t)
For such f and g you should be able to compute P(s) and H(s) in
closed-form. Extracting h(t) is likely to be problematic though. See
ftp://physics.uwa.edu.au/pub/Mathematica/MathGroup/LaplacePulseTrain.nb
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
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