powershape
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## powershape

powershape — Waveshapes a signal by raising it to a variable exponent.

## Description

The powershape opcode raises an input signal to a power with pre- and post-scaling of the signal so that the output will be in a predictable range. It also processes negative inputs in a symmetrical way to positive inputs, calculating a dynamic transfer function that is useful for waveshaping.

## Syntax

    aout powershape ain, kShapeAmount [, ifullscale]

## Initialization

ifullscale -- optional parameter specifying the range of input values from -ifullscale to ifullscale. Defaults to 1.0 -- you should set this parameter to the maximum expected input value.

## Performance

ain -- the input signal to be shaped.

aout -- the output signal.

kShapeAmount -- the amount of the shaping effect applied to the input; equal to the power that the input signal is raised.

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

To avoid discontinuities, the powershape opcode treats all input values as positive (by taking their absolute value) but preserves their original 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 (before final scaling) will also be within this range for positive shaping amounts and providing a smoothly evolving transfer function while varying the amount of shaping. Values of kShapeAmount between (0,1) will make the signal more "convex" while values greater than 1 will make it more "concave". A value of exactly 1.0 will produce no change in the input signal.

## See Also

pow, powoftwo

## Examples

Here is an example of the powershape opcode. It uses the file powershape.csd.

Example 711. Example of the powershape opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in
    -odac           -iadc    ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o abs.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>
    instr 1
    	imaxamp    =           10000
    	kshapeamt  line        p5, p3, p6
    	aosc       oscili      1.0, cpspch(p4), 1
    	aout       powershape  aosc, kshapeamt
    	adeclick   linseg      0.0, 0.01, 1.0, p3 - 0.06, 1.0, 0.05, 0.0

    		     out         aout * adeclick * imaxamp
    endin

    </CsInstruments>
    <CsScore>
    f1 0 32768 10 1

    i1 0 1    7.00  0.000001 0.8
    i1 + 0.5  7.02  0.01   1.0
    i1 + .    7.05  0.5    1.0
    i1 + .    7.07  4.0    1.0
    i1 + .    7.09  1.0    10.0
    i1 + 2    7.06  1.0    25.0

    e

    </CsScore>
    </CsoundSynthesizer>

## Credits

Author: Anthony Kozar
January 2008

New in Csound version 5.08

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