[sdiy] Re: linear FM

[Ian Fritz]

>Hmm, reversing the direction of current flow thru a capacitor doesn't
>mean reversing frequency. Actually, a triangle wave is a mix of many
>partials, all with their own frequencies (if you're using a fourier
>series). And while it's certainly convenient to speak of "phase" to
>describe a fraction of a triangle cycle (just as you would for a sine
>wave), I'm not sure if this can be backed up mathematically at all.
>I guess it's all just a matter of definitions. But does this equation
>f = d_phi/d_t make sense for any other waveform than a sine?


Unless I misunderstand your question, the answer is emphatically *YES*.

Any periodic-in-time function can be written mathematically in the form

y(t) = f(wt - a),

with the condition

y(t + T) = y(t)

defining the periodicity.

The phase is p = wt - a,

and its derivative is the frequency

dp/dt = w.

The function f is arbitrary.

This is a minor simplification of the general d'Alembert formulation 
of  traveling waves as

y(x , t) = f(ct - x) + g(ct + x),

with f and g arbitrary (even nonlinear) functions.

I hope I answered what your question was, not just what I imagined it to be!

   Ian