[sdiy] Re: Walsh Generator Release!!!

[Magnus Danielson]

From: "Maciej Bartkowiak" <mbartkow at et.put.poznan.pl>
Subject: Re: [sdiy] Re: Walsh Generator Release!!!
Date: Tue, 2 Apr 2002 11:42:42 +0200

> John,

Maciej,

> > Fourier says that any peroidic wave is composed of an infinite series of
> > harmonically related sine waves. Walsh says that any periodic wave may be
> > composed of an infinite series of any other shaped wave.
> 
> Actually, it's not Walsh but Fourier-Euler theorem, that states any periodic
> waveform may be obtained by summing infinite orthogonal series of functions.
> These functions may be of arbitrary shape, provided they are "normal"
> (i.e. normalized in their energy over period) and form a complete set (in
> order
> to fulfill Parseval's equation). Fourier-Euler generic formula tells how to
> obtain
> these coefficients of Fourier series for any base function, not only a
> harmonic one.
> It's a tradition to associate harmonic series with Fourier, though, because
> Fourier
> gave such an example application of his theorem.

Right.

What Fourier was actually doing when he came up with his stuff, was to
analyse the heat transmission in metal rods. This is however a
completely different subject. He was also laugthed out of the French
academy of science for his theorem that one could form any periodic
waveform by summing up a number of weighed sines and cosines.

> Important point to note is harmonic waves are interesting for analysis of
> electronic
> circuits and mechanical devices, because a harmonic wave is a generic
> solution
> of a simple first-order differential equation that describes basic
> relationship in RLC
> circuits, a vibrating spring, a pendulum etc.

Um... no!

Fourier doesn't work on classic RLC stuff, but if you drop the R it
works!

You need LaPlace to handle the diminishing amplitude of an
RLC. Fourier ONLY covers sine/cosine based waveforms. Given its
period, the amplitude may not change for any of the periods. If it
does (and it allways does BTW) then the Fourier theorem, transform
etc. does not have the matematical guts to analyse it. This is a
classic case of missapplying Fourier, which I keep raving about.
It is sad to see that not too many people recognice and understand
this fundamental flaw in many arguments.

Also, being a nitpick as I am, having both a L and a C actually forms
a second order linear system.

> From the point of view of sound synthesis, harmonic series is probably the
> most boring one.

Yeap.

Cheers,
Magnus