[sdiy] Re: Walsh Generator Release!!!

[John L Marshall]

So you have met TIM distortion.

----- Original Message -----
From: Magnus Danielson <cfmd at swipnet.se>
To: <mbartkow at et.put.poznan.pl>
Cc: <synth-diy at dropmix.xs4all.nl>
Sent: Wednesday, April 03, 2002 10:47 AM
Subject: Re: [sdiy] Re: Walsh Generator Release!!!


> 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