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)}
>
>
> 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
School of Physics, M013                         Fax: +61 8 9380 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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