[sdiy] spiral waveform

[Ian Fritz]

Hey Folks --

The concept of spiral waveforms seems fairly straightforward.

Circular waves  --  sine and cosine -- can be represented as a projection, 
along a single direction, of the motion of a point around a circle.  A 
simple 2D to 1D mapping.  This should be familiar to many as the spinor 
representation of signals.

A spiral wave, then, is a similar projection of a point moving along a 
spiral.  Imagine, for example, a point moving along two loops of a spiral 
and then jumping back to the beginning to start the next wave cycle.  The 
sin-like projection of this motion will be continuous, with a change in 
slope, at the origin.

The exact nature of the wave depends on whether the point is moving with 
constant angular velocity or with constant linear velocity (or even 
something else).  In the constant linear velocity case, the "instantaneous" 
frequency will be smallest at the outside of the spiral and largest at the 
inside.  In the constant angular velocity case the "instantaneous" 
frequency is constant.  In both cases the instantaneous amplitude varies as 
the distance of the generator point from the center of the spiral.

The trickiest part of an analog implementation would seem to be dynamically 
changing the waveshape, i.e., keeping the wave period constant as the shape 
of the spiral changes.  However, simple cases are easily realized.  For 
example, a sine wave multiplied by a sawtooth, dynamically mixed with the 
original sine, might be taken as a rudimentary prototype.

I know many of you were unhappy with the tone of the original poster, but 
myself I would rather have a discussion of a novel waveshaping technique 
than the constant rehashing of old dross, such as the difference between 
the 4016 and 4066.

Here is an informative page on AS: http://www.udel.edu/bkirby/asperger/
Can't we be a bit more tolerant of those less fortunate than ourselves?

   Ian