polynomial — Efficiently evaluates a polynomial of arbitrary order.
The polynomial opcode calculates a polynomial with a single a-rate input variable. The polynomial is a sum of any number of terms in the form kn*x^n where kn is the nth coefficient of the expression. These coefficients are k-rate values.
ain -- the input signal used as the independent variable of the polynomial ("x").
aout -- the output signal ("y").
k0, k1, k2, ... -- the coefficients for each term of the polynomial.
If we consider the input parameter ain to be "x" and the output aout to be "y", then the polynomial opcode calculates the following equation:
y = k0 + k1*x + k2*x^2 + k3*x^3 + ...
Here is an example of the polynomial opcode. It uses the file polynomial.csd.
Example 772. Example of the polynomial 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 -odac ;;;realtime audio ;-iadc ;;;uncomment -iadc if realtime audio input is needed too ; For Non-realtime ouput leave only the line below: ; -o polynomial.wav -W ;;; for file output any platform </CsOptions> <CsInstruments> sr = 44100 ksmps = 32 nchnls = 2 0dbfs = 1 ; The polynomial y=x^n where n is odd always produces a curve ; that traverses the range [-1, 1] when the input is within ; the same range. Therefore, we can use one of these curves ; to make a nonlinear phasor that repeatedly reads a table ; from beginning to end like a linear phasor (maintaining ; continuity) but that distorts the waveform in the table. instr 4 ; This instrument demonstrates phase distortion with x^3 idur = p3 iamp = p4 ifreq = p5 itable = p6 aenv linseg 0, .001, 1.0, idur - .051, 1.0, .05, 0 ; declicking envelope aosc phasor ifreq ; create a linear phasor apd polynomial aosc, 0, 0, 0, 1 ; distort the phasor with x^3 aout tablei apd, itable, 1 ; read a sine table with the nonlinear phasor outs aenv*aout*iamp, aenv*aout*iamp endin instr 5 ; This instrument demonstrates phase distortion with x^11 idur = p3 iamp = p4 ifreq = p5 itable = p6 aenv linseg 0, .001, 1.0, idur - .051, 1.0, .05, 0 ; declicking envelope aosc phasor ifreq ; create a linear phasor apd polynomial aosc, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ; distort the phasor with x^11 aout tablei apd, itable, 1 ; read a sine table with the nonlinear phasor outs aenv*aout*iamp, aenv*aout*iamp endin instr 6 ; This instrument crossfades between a pure sine and one distorted with x^11 idur = p3 iamp = p4 ifreq = p5 itable = p6 aenv linseg 0, .001, 1.0, idur - .051, 1.0, .05, 0 ; declicking envelope aosc phasor ifreq ; create a linear phasor aout3 tablei aosc, itable, 1 ; read a sine table without the linear phasor apd11 polynomial aosc, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ; distort the phasor with x^11 aout11 tablei apd11, itable, 1 ; read a sine table with the nonlinear phasor kamount linseg 1.0, 0.05, 0.9, 1.0, 0.0 ; crossfade between two outputs aout = aout3*kamount + aout11*(1.0 - kamount) outs aenv*aout*iamp, aenv*aout*iamp endin </CsInstruments> <CsScore> f1 0 16385 10 1 ; sine wave ; descending "just blues" scale t 0 100 i4 0 .333 .7 512 1 i. + . . 448 i. + . . 384 i. + . . 360 i. + . . 341.33 i. + . . 298.67 i. + 2 . 256 s t 0 100 i5 0 .333 .7 512 1 i. + . . 448 i. + . . 384 i. + . . 360 i. + . . 341.33 i. + . . 298.67 i. + 2 . 256 s t 0 100 i6 0 .333 .7 512 1 i. + . . 448 i. + . . 384 i. + . . 360 i. + . . 341.33 i. + . . 298.67 i. + 2 . 256 e </CsScore> </CsoundSynthesizer>