I said:
"Analogue" and "digital" are words most people dont understand..
Christopher replied:
"For me it is natural (nature) verses un-natural, then that raises other questions? Digital functions with square waves but does not necessarily mean square waves are always digital, just square."
"Natural" and "un-natural" - Oh hell - The number of times I have engaged in argument over these words.. (mostly with judgmental moralists, including my father who regarded "un-natural" as "sinfull" - And un-natural was anything he or his god didnt like - always "strange" to me that rarerly, if ever, are peoples personal 'likes' and 'dislikes' different to thier gods 'likes' and 'dislikes' ;-) Even at £1 a time, I probably wouldnt have any financial worries now if I had been paid.. But the bottom line is this, like it or lump it, NOTHING is "un-natural" .. Right down to QP , everything which can happen does happen - everything which does happen is determined by nature and is therefore "natural", and, as everything which can happen does happen, everything which happens is all that can happen! - so everything is "natural" ! ;-)
Let me explain how I think about "Digital" "Analogue" and "Mixed signal" - my "understanding" or "perspective" if you like:
Binary signals:
There is no difference between a square wave and a binary ("digital") signal in terms of its voltage levels - Generally, one thinks of digital in terms of binary, as in, "two state". I will ignore for a moment the fact that there is no such thing as a truly "binary" signal, that "analogue" "invades" everything (there is always a transition slope when a physical device goes from one state to another) then every square wave can be regarded as a binary ("digital") signal - it has 2 voltage states, one being regarded as "low" or a logic 0, and one being regarded "high" or a logic "1".
There is no difference between a square wave generated by a couple of transistors in a multivibrator, or generated by feeding a sine wave into a comparator (as with the Theremax) or generated by a pin on a MCU driven by software which flips this pin from "1" to "0", in terms of the fact that these are all signals which have two possible amplitude states only.
However, there is some murky water - "water" which, IMO, makes defining "binary" as equivalent to "digital" somewhat inaccurate..
Mixed Signals:
In terms of amplitude, Binary signals are constrained to two levels - However, one can have a square wave which has an entirely unconstrained frequency - This can probably be easiest seen (in terms of theremins) if one takes a VFO whose frequency is changed as a function of antenna capacitance, and can be ANY value within its designed range.. The amplitude (level) and shape of this waveform may vary, so its "Y" axis can be analogue - Its frequency can vary, so its "X" axis is analogue..
Now, if we take the above VFO signal, and feed it into a correctly designed comparator, we get a square wave out from this comparator - This square wave has BINARY output levels - All analogue data from the input signals "Y" axis (the wave shape and amplitude levels) is lost.. However, the input signal analogue data on its "X" axis (its frequency) is retained and "duplicated" on the square wave from the comparator, whos "X" axis will still be "analogue".
This, to me, is a "mixed signal".
Mixed signals can be processed by binary computation elements and still retain the analogue "X" components - This processing can be simple (XOR "heterodyning" is the simplest example I can think of) or more "complex" .. (see my "Mixed signal waveshaping" post on Element-14)
"Mixed signal" covers a huge area of essential electronics and theremin implementations - The Theremax square wave generator is mixed signal, the E-Pro deviders and XOR are mixed signal.. Neither of these theremins are digital! - They are MIXED SIGNAL, or at least employ some mixed signal elements... And of particular note is that these "mixed signals" are directly involved in the actual audio generation or audio signal path.
So - Whats "Digital" ?
Digital, to me, for practical purposes, is where both axis (X and Y) are numerically constrained - If one has a VFO and feeds this into a circuit where it is processed, and where (for example) the VFO frequency is "chopped" into 1 cent "quantities" , and the analogue "Y" data is discarded, and from this an audio waveform is constructed, then one has a digital system - All analogue data has been "quantized".. The required data has been extracted from the input signal/s, converted into numerical (Digital) form, processed by digital computation elements, and used to produce audio output based on the input data.. All aspects of the processing and output data are constrained to the resolution available to the processor and its components, both on the "X" and the "Y" axis..
The above "constraints" were a problem in the past - Processor speeds and bit depth made it difficult or impossible to cleanly resolve pitch data without "zipper" effects, and there were many problems - But modern processors and FPGA's etc are probably now capable of implementing a theremin where numeric constraints are below the level where they can be noticed.
I have not yet seen a digital theremin on the market (not saying there arent any - but I aint seen any that I know of - perhaps there may be some which are pretending to be analogue !) - Dewsters theremin is the only demo of a truly digital theremin that I have definately seen.