2007/12/5, Anthony Kozar <anthonykozar@sbcglobal.net>:

Victor.Lazzarini@nuim.ie wrote on 12/5/07 2:54 AM:

> PD seem useful. UDOs are also good because they're didactical, can you
> do both?

Thanks.  I wrote the phase dist. opcodes (and powershape below) a while ago
but I will make UDOs too.

> How do the waveshaping opcodes you mention
> differ from simply building them with oscillator and table
> lookup?

They allow for _dynamic_ waveshaping where the transfer function varies over
time.  I have written the following opcodes so far and hope to come up with
some more:

aout  powershape    ain, kShapeAmount [, ifullscale]
aout  polynomial    ain, ka0 [, ka1 [, ka2 [...]]]
aout  chebyshevpoly ain, ka0 [, ka1 [, ka2 [...]]]

polynomial efficiently calculates any single-variable polynomial with k-rate
coefficients.  chebyshevpoly does the same but each coefficient is a
multiplier for an nth-order chebyshev polynomial.  With a sine wave input,
this allows precise time-varying control over any number of
harmonically-tuned partials, but requires only one oscillator.

Manual description for powershape:

This opcode is very similar to the pow unit generators that already exist in
Csound for calculating the mathematical "power of" operation.  However, it
introduces a couple of twists which I think make it much more useful for
waveshaping audio-rate signals.  The kShapeAmount parameter is the exponent
to which the input signal is raised.

Normally, unless the exponent is an odd integer, the pow() of a negative
input is a complex number, so the Csound ugens simply return zero in those
cases.  This will turn a bipolar audio signal into a unipolar signal with
large portions of the output pinned to zero.  The powershape opcode instead
treats all input values as positive but preserves their sign in the output
signal.  This allows for smooth shaping of any input signal while varying
the exponent over any range.  (Powershape also (hopefully) deals
intelligently with  discontinuities that could arise when the exponent and
input are both zero.  Note though that negative exponents will usually cause
the signal to exceed the maximum amplitude specified by the ifullscale
parameter and should normally be avoided).

The other adaptation involves the ifullscale parameter.  The input signal is
divided by ifullscale before being raised to kShapeAmount and then
multiplied by ifullscale before being output.  This normalizes the input
signal to the interval [-1,1], guaranteeing that the output will also be
within this range.  Also, the pow() function provides a smoothly evolving
transfer function when its input is in this range.  Values of kShapeAmount
between (0,1) will make the signal more "convex" while values greater than 1
will make it more "concave" and a value of exactly 1.0 will produce no
change in the input signal.

Anthony Kozar
anthonykozar AT sbcglobal DOT net
http://anthonykozar.net/

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