[sdiy] PM vs FM was: Re: Buchla 295 10-band comb filter topology

[brianw]

This is all excellent, but...

k does not need to be time-dependent because it is multiplied by t. kt and/or kwt are already time-dependent because the value is different for every t (for every sample), even though k remains the same.

Just to be clear, the accumulator exists because of t. The constant, k, merely allows the accumulator to progress at different rates.

Brian


On Nov 28, 2022, at 9:42 AM, Ian Fritz wrote:
> OK, I've figured out what the FM/PM disagreement most likely stems from.
> 
> On Fig 8 of the patent the DX7 output is given by the expression
> 
> Sin{kwt + f(w_m t)}
> 
> From fundamental theory, this expression is THE SAME for FM and PM. The difference between the two is in the function f().
> 
> For FM the function f is proportional to  delta(w)/w_m, where delta(w) is the maximum frequency deviation and w_m is the frequency of the modulating signal.
> 
> For PM f is proportional to just delta(w) itself.
> 
> Once again, these are textbook results: standard and well known. Their derivation can be found in any good text on radio theory.
> 
> I remember looking at the PM/FM question some time ago and being stopped because Yamaha never seemed to say explicitely what the definition of f is. Now I think it is given by the algo I outlined in my previous post. {NB k must have a different meaning here, and of course it must be time dependent or there would be no need for the accumulator.}
> 
> I'm enjoying this discussion, too, and would love to hear more comments from folks who have studied the theory.
> 
> Ian