Hi all,

Of course I'm aware of it this work probably won't give m a (bit late) YUP existence in SanFrancisco or a well paid Berkeley professorship that I like, but at least I don't really run the risk of looking like a dumb-*ss when playing the unpaid professor a bit in this territory, and hopefully cut down some Non-Giant Redwood trees that appear to create more pollution than oxygen.

First, a repeat of what I've tried to communicate a number of times, as it were to discourage the idea of taking interesting mathematical truths from (lame or interesting) digital signal processing effects in music, let's first consider the theoretical basics that defy all ignoration:

{Digital System} --> {Digital Sample stream} --> {Digital to Analog} --> {Analog signal}

, versus:

  {Analog System} --> {Analog Signal}

The main differences are on a short list:

(1) The only way in which the two analog output signals of graph (A) and (B) are going to be (almost or perfectly) the same is when somehow the digital system creates very well made samples (which *CAN* come from simply playing back accurately sampled form of some frequency limited signal), and the Digital to Analog convertor is very high quality (or to achieve actual mathematical perfection: is a perfect reconstruction type) (2) The digital system implemented as a filtering of any kind of combination of FIR/IIR tap-connections is normally not coming close to making analog-equivalent signals, by far, unless it is big, and there explicit measures being taken (extremely high sampling frequencies and vertical resolution, tuning of the DA-convertors always-present transient behavior, medium long averaging effects control (hard problem) seriously long sinc-based integral corrections (computationally intensive)). (3) Reconstructing an analog signal from samples that isn't a retarded subset of all possible signals, will require a DA convertor design which has a serious signal delay, for all known normal and industrial Audio convertors. So to prevent some very measurable (by over see-ably simple traditional measurement techniques at the level of the THD of a very moderate transistor radio) distortion, serious measures would have to be taken, like outside the scope of this list. Even making sure those distortions don't become multi-fold ugly and even a potential danger to the hearing of the customers isn't easy (and thus far never has been discussed, even though these distortions are almost incredibly ugly, and host of unrealistic monitors have been "invented" which are supposed to smooth some of this over, apparently through lack of awareness of the impossibility to approach per-sample sinc functions by any resonance or other mechanical or switching amp trick). (4) It is quite possible to create a computer simulation of an electronics circuit, like a Moog filter, even with serious accuracy, and to state the output of such simulation in the form of a sequence of equidistant digital samples with accurate vertical quantization. Even this does not preclude you from having to take equal relevant care of the above, except for point (2).

There, that's a few "New" things, apparently for those not blessed with either the intelligence, means or geographical or time opportunity to follow a good EE university (or for most of this: bachelor level) Sophomore year equivalent.

Of course going a bit further in the better EE education (say second or third year of a serious education), you may want to practice yourself in creating computer models of interesting non-linear electronics circuits, and see if you computer simulations on the basis of these models and some form of circuit-to-signal strategy, be it based on the frequency domain or not, turn out to be accurate, and maybe invent some fun games with this, like a "Virtual Prophet-5" that everybody can run on their home computer for free, or things equally thrilling and educational!

I had done some (extremely low budget) preparatory work because of my much longer standing personal interests for this (like owning various synthesizers and samplers with digital filters like the TG500 in the 80s), see eg http://theover.tripod.com/so1.html and http://theover.tripod.com/switch.html , written before the year 1999.

Ir. T. Verelst

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