[sdiy] Re: Walsh Generator Release!!!

[Magnus Danielson]

From: Magnus Danielson <cfmd at swipnet.se>
Subject: Re: [sdiy] Re: Walsh Generator Release!!!
Date: Thu, 04 Apr 2002 01:59:04 +0200 (CEST)

Maciej,

A clarification...

> > Both Laplace and Fourier transforms are complementary,
> > no one is a generalization or simplification of the other. The
> > domain of Laplace transform is a complex halfplane, but it
> > is limited to signals starting from zero, so you are basically
> > limited to the analysis of transients.
> 
> Actually, it is not limited to zero, this is just the assumption that
> comes with the assumption of the transient. It all comes down to
> causuality and this just must assume for the linear system you
> analyse. Basically, if you have a system which gets an input signal at
> time t, then due to causuality there can be no output of the system
> correlating to that event prior to t, i.e. that output must be assumed
> to be 0 up to the time t. The time integral from minus eternity to
> (but not including) time t can thus be safely assumed to be exactly 0,
> and we does not have to integrate over that time and thus we can start
> at the time t. For practical reasons the time t has been selected to
> be 0. If we do not assume the impulse, but rather views a continous
> signal, then we must integrate from minus eternity to eternity, since
> it all applies. This happends to rule out the amplitude change in
> practice, so we end up with only frequency terms, which comes out to
> be the Fourier transform case.

This last sentence... "This happends to rule out the amplitude change
in practice" should not be confused with the theoretical case, where
the amplitude change may still be fully valid. Nothing can be
concluded as such from it. However, for many real systems, it is an
unnatural case.

It nagged me it's wasn't quite right.

Cheers,
Magnus