[sdiy] Re: Walsh Generator Release!!!

[Maciej Bartkowiak]

John,

> 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.

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.

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

MB