"So why heterodyne? Is it expensive to derive numbers directly from an RF signal?" GordonC
Yeah, it has been covered ;-) ..
With RF one has a high frequency varying by a tiny percentage, perhaps 5% or less, and one has extremely small period, so if one wants to capture this 5% from the period variation by determining its 'length' and deducting the baseline "ref Osc" value, you could need a clock up in the 100's of Ghz probably.
You can devide the RF down, say to 1kHz mean - but even doing this one doesnt get the required pitch resolution (14 bits or more) without an extremely high frequency counting clock..
However - If you heterodyne the front-end oscillators, you get rid of all the unwanted data (end up converting the 5% to 100%) - you end up with a frequency from which you can get the numbers without excessive clocks etc.
The most recent posts on Dewsters "digital theremin" thread are dealing with some of this at quite a basic level right now! - And perhaps almost every aspect of the "how do we get the numbers" issue has been discussed there - a lot of it you will probably understand better than I do, because I think your maths comprehension is better than mine! .. I also think its been discussed in the "open theremin" thread.
I would love it if someone would collate important technical matters like this which are spread all through TWs database, into documents or folders - I think this could be one of the most useful technical repositories on the web, and not just for theremins!
Fred.
For me, there are just 2 ways to get the numbers - One is using an analogue scheme like a filter (or PLL as in my "upside down" topology) to generate a voltage from the circuit tuned to resolve the RF frequency variation, the other is to use heterodyning or variants thereof.. I know there are other ways, but they are nearly too complex for me to get my head 'round, and certainly too complex for me to implement!