[sdiy] Generating acyclic waveforms?

[Jerry Gray-Eskue]

I am not quite sure how to express this properly but here is a shot at it:

A signal v(t) is periodic with period T if

	v(t) = v(t+T) for all t
	In other words the waveform is precisely repeating over the period T.

The Fundamental sine wave  v(t)= Vo cos(wt+ phase angle). ( or is that a
cosine wave? )
v(t) is +- around zero and the Sum of (v(t) over the period T) = 0.


Now if we take the first harmonic its value is vh(t)= Vo cos(wt+ (phase
angle * 2)).
So if we vary the Harmonic thus  vh(t)= Vo cos(wt+ ((phase angle +
SomeFunctionOf(v(t))* 2)).
That is the harmonic is frequency shifted using the fundamental sine's v(t)
as the control.
Assuming this is a sine not cosine wave, we have the phase angel accelerated
during the first T/2 and decelerated during the second half with a net
acceleration of zero.

So the waveform repeats each T and

Vo cos(wt+ ((phase angle + SomeFunctionOf(v(t))* 2)) = Vo cos(w(t+T)+
((phase angle + SomeFunctionOf(v(t+T))* 2)).


Clear as mud???

- Jerry

-----Original Message-----
From: Ian Fritz [mailto:ijfritz at comcast.net]
Sent: Monday, March 22, 2010 2:51 PM
To: Jerry Gray-Eskue; Synth-diy at dropmix.xs4all.nl
Subject: Re: [sdiy] Generating acyclic waveforms?


At 01:00 PM 3/22/2010, Jerry Gray-Eskue wrote:

>I may be misunderstanding what "stretched harmonic spectra" actually means,
>but if we take a sine wave fundamental frequency and a set of harmonics,
and
>use the fundamental sine wave to frequency shift (+- around zero) the
>harmonics we would get a "precisely repeating waveform" with "inharmonics".

I may not understand correctly what you are saying.  But if you add together

Sin ((w+eps)t) + Sin (2wt)

You do not get a steady repeating waveform.

Ian