[sdiy] Re: Walsh Generator Release!!!

[Magnus Danielson]

From: Maciej Bartkowiak <mbartkow at ET.PUT.Poznan.PL>
Subject: Re: [sdiy] Re: Walsh Generator Release!!!
Date: Wed, 03 Apr 2002 11:43:56 +0200

> Magnus

Maciej,

> > Fourier doesn't work on classic RLC stuff, but if you drop the R it
> > works!
> 
> Alright, I was too generic. The response of RLC circuits is composed of
> damped sines and cosines and in case of lossy circuit (any R!=0) is 
> aperiodic, so Fourier series do not apply. What I wanted to say is that 
> harmonic functions are invariables of RLC circuits, i.e. you can analyse 
> those circuits by passing various sines and cosines through them (hence 
> the concept of Fourier transmitance).

Ah, well, you can analyse their behaviour by tossing sine signals
through them, measuring the amplitude and phase change. Doing this for
a multitude of frequencies (like in a network analyser) gives you
curves which which you may deduct the probable characteristic. If you
however would be measuring with accelerating and retarding amplitudes
as well, you could get more information out, like better discovering
the poles and zeros of all-pass functions.

> > 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.
> 
> This time you went too far. Fourier transform is perfect for analysis 
> of nonperiodic functions. It may be not a good tool for analyisng
> circuits, but is an ideal tool for analyisng transient signals.

No. I have first hand experience on this, and it is well covered in
literature as well. Fourier transforms (in its strict sense) not at
all as good as we want it. We tend to use weighting windows to
overcome some of the defficiencies of doing _just_ Fourier
transformation. Fourier analysis/transforms is the main tool, but I
claim it is overused and overrated, much since people actually THINK
it is perfect. What happends is that you will transform what can
essentially be viewed as a constant amplitude variant of the signal,
and the difference between the actual signal and the constant
amplitude variant of the signal. This differens signal will spread
itself all over, causing "noise" to the measurement. The
weigh-functions tries to heal some of it by making the odd ends less
important than the center.

The missapplication of Fourier transforms cause obstruction of data in
real life, in many forms of measurements. So, I don't think I went too
far, I have actually spent quite some time thinking about this.

I am not saying that Fourier transform is useless, not at all, but I
say it has been over-rated and does not have the mathematical guts of
the LaPlace transform which covers all of the Fourier transform, and
more. There are stuff which the LaPlace can't handle either, and that
is non-linearity like variable systems, but that is another step up
the ladder.

For me the Fourier analysis is inadequate for propper understanding of
the linear behavior when discussing audio signals. The transients of
the music can be so much different even if you have a fairly "flat"
responce-curve.

Cheers,
Magnus