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 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul