tri 2 saw modualtion

[Eli Brandt]

Don Tillman wrote:
> If you look at the harmonic spectra of the waveform you'll see for the
> triangle case that every even harmonic is nulled out, and as you
> change the symmetry, those "nulls" will slide up in frequency over the
> harmonics and move farther apart, up until the wave is a full sawtooth
> shape where there are no more nulls.  A Bessel function describes the
> amount of each harmonic.
> 
> (This is a guess from the harmonic spectra of a PWM square wave -- I
> haven't done the actual math.  The same mechanism applies though.)

A triangle-saw sweep is the integral of a square-pulse sweep (if all
of your pulse waves have the DC properly stripped out), so the nulls
are in the same place and all.  But the spectrum is tilted 6dB/oct.

Do you know how to analyze a PWM sweep?  Hmm, I'm thinking of a
rectangular waveform as the integral of the sum of two oppositely-
polar pulse trains.  Then width modulation corresponds to modulating
the pulses' phase offset.  But the cancellation here looks rather like
a flanger's, which neither involves Bessels nor sounds quite like PWM.

Another for the synth list: the Matrix-N family has saw/tri modulation
on the audio oscs.  I've never looked at the waveform, though.

-- 
     Eli Brandt  |  eli+ at cs.cmu.edu  |  http://www.cs.cmu.edu/~eli/