[sdiy] Re: linear FM

[Ian Fritz]

At 09:13 AM 2/5/2003, jhaible at debitel.net wrote:

>(But ... there is also a definition of phase for each harmonic, if you
>develop the periodic waveform into a fourier series.
>
>How do these two definitions fit together ? Especially when you apply
>linear FM to an oscillator with a waveform that's different from sine?
>
>And, if we use our oscillator waveform - triangle, saw etc. - as an
>input for a sine shaper, would it matter at all? (I don't think so).)

For the unmodulated case the phase question is straightforward. The phase 
of the n-th harmonic varies at n times the rate of the phase of the 
fundamental. The initial phase of each harmonic comes directly from the 
Fourier analysis.  For example, it would be the arctan of the ratio of the 
sin and cos coefficients of the n-th component, if that particular (real) 
Fourier form were used.

I won't try to answer about the modulated case, but Bernie gave a nice 
derivation in the MEH (chapter 2).

>My original point was that as long the oscillator is unmodulated,
>there is no change from positive to negative frequency (and thus
>no switch from increasing phase to decreasing phase), regardless
>of the waveform that's used in the VCO core.

That sounds correct.

   Ian