[sdiy] Howdy

[Chris Stecker]

On Monday 29 July 2002 11:34 am, Marc Jordan wrote:
> Oh, man.  Is this gonna be like the Mac forums? :)

Yes?

This is a little weird.  If information rate is to be a useful concept in 
signal processing, estimates of it for analog signals must be made with 
respect to the noise characteristics and frequency response of the system 
under study.   It is incorrect to posit that (any) analog-level / 
continuous-time system has a higher information rate than (any) 
quantized-level / discrete-time representation, just as it is incorrect to 
assume that digital representations are "cleaner" or "more precise" than 
analog representions.  If you understand the limiting factors in your analog 
signal, you can devise a quantized/discrete encoding that DOES NOT lose 
information.  That is not to say that commonly-adopted standards for sampling 
rate and quantization in recording are necessarily sufficient, of course, and 
there are many examples of (particular) analog/continuous systems with higher 
fidelity than (particular) digital/discrete systems.

Digital signal representation reflects a mathematical model of a signal.  
An analog circuit, by itself, possesses no such intrinsic representation.  
However, analog circuit designers do use mathematical description of signals 
in the design process, including (for example) frequency-domain 
representations based on Fourier's theory.  Extensions of those concepts show 
that signals can be completely specified as mixtures of a sufficient number 
of basis functions.  In Fourier analysis, the basis functions are sinusoids, 
which makes convenient the analysis of signals by their frequency content.  
In sampling theory, the basis functions are commonly square impulses.  These 
are localized in time, making some other kinds of operations more convenient. 
Mathematically, the choice of basis function doesn't matter; any appropriate 
set will allow as precise a reconstruction of the original signal as 
required.  The different approaches simply assist the designer in 
understanding and/or manipulating the signal in different ways.  This may 
have a profound impact on the practical design of a circuit, its fidelity, 
artifacts, etc., but the mathematical representation is not, by itself, at 
fault.  Unless you are prepared to claim that analog circuit designers do not 
base their designs on mathematical analyses of signals, there is no 
_theoretical_ difference between the approaches, simply a practical one.

However, I agree that using the term "bleeding edge" to refer exclusively to 
digital technology is disingenuous, particularly in a forum like sdiy.

-Chris


>
> -----Original Message-----
> From: Grant Richter [mailto:grichter at asapnet.net]
> Sent: Saturday, July 27, 2002 1:21 PM
> To: Oren Leavitt; Marc Jordan
> Cc: Synth (E-mail)
> Subject: Re: [sdiy] Howdy
>
> > from vacuum-tube synths to 'bleeding edge' digital technology to
> > old-school 1970's analog modulars to early digital synths to Theremin
> > to.........well just about anything you could possibly NOT imagine...
>
> As a personal note...
>
> It is well understood mathematically that when information is sampled
> and/or quantized, the information content (entropy) is reduced. While
> digital methods are the current craze, the results are inherently
> information reduced in comparison to analog generation methods. From a
> mathematical perspective, continuous time computation contains a much
> larger information rate than discrete time computation. This is precisely
> why discrete time computation is used, to reduce the information rate to
> levels that can be computed by digital methods.
>
> Analog methods inherently compute with continuous levels in continuous time
> with a much larger overall information content.
>
> The difference boils down to sacrificing data rate to gain an increase in
> precision for describing any arbitrary data point. But the process of
> sampling and quantization produce audible artifacts that some people
> dislike.
>
> The perception of "old school" vs. "bleeding edge" is really the product of
> an over generous marketing campaign for a technology based on mathematics
> from the 1850's (George Boole).
>
> On synth-DIY, there is a great deal of "bleeding edge" analog design
> happening every day.