puredata-doc 0.43.0-4 / usr / lib / puredata / doc / 3.audio.examples / E05.chebychev.pd

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#X text 203 198 2nd C.P.;
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#X text 259 51 This patch computes Chebychev polynomials and stores
them in a wavetable for use later.;
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#X text 497 45 calculate;
#X text 495 64 Chebychev;
#X text 496 83 polynomials;
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#X text 134 2 waveshaping with Chebychev polynomials;
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#X text 107 256 This patch demonstrates using Chebychev polynomials
(of the first kind) to generate pure harmonics using waveshaping. The
pure harmonic only comes out when the index is one (top of the scale).
Smaller indices will give various mixes of harmonics. The table initially
holds the fifth Chebychev polynomial \, so you can get the fifth harmonic.
;
#X text 106 355 There is an audible "rolling" sound as the index changes
for the higher degree polynomials \, because the amplitudes of the
lower partials can rise and fall several times apiece as the index
rises from zero to one.;
#X text 105 422 Indices greater than one will try to read values outside
the table (which would be clipped appropriately). Anyway \, the polynomials
increase rapidly in value outside the interval from -1 to 1 that we
are using here.;
#X text 106 491 When you get tired of Chebychef polynomials you can
draw your own functions by hand and/or try other formulas.;
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