GEN03
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## GEN03

GEN03 — Generates a stored function table by evaluating a polynomial.

## Description

This subroutine generates a stored function table by evaluating a polynomial in x over a fixed interval and with specified coefficients.

## Syntax

    f  #  time  size  3  xval1  xval2  c0  c1  c2  ...  cn

## Initialization

size -- number of points in the table. Must be a power of 2 or a power-of-2 plus 1.

xval1, xval2 -- left and right values of the x interval over which the polynomial is defined (xval1 < xval2). These will produce the 1st stored value and the (power-of-2 plus l)th stored value respectively in the generated function table.

c0, c1, c2, ..., cn -- coefficients of the nth-order polynomial

C0 + C1x + C2x2 + . . . + Cnxn

Coefficients may be positive or negative real numbers; a zero denotes a missing term in the polynomial. The coefficient list begins in p7, providing a current upper limit of 144 terms.

| Note
The defined segment [fn(xval1), fn(xval2)] is evenly distributed. Thus a 512-point table over the interval [-1,1] will have its origin at location 257 (at the start of the 2nd half). Provided the extended guard point is requested, both fn(-1) and fn(1) will exist in the table. GEN03 is useful in conjunction with table or tablei for audio waveshaping (sound modification by non-linear distortion). Coefficients to produce a particular formant from a sinusoidal lookup index of known amplitude can be determined at preprocessing time using algorithms such as Chebyshev formulae. See also GEN13.

## Examples

Here is an example of the GEN03 opcode. It uses the file gen03.csd.

Example 981. Example of the GEN03 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 out
    ;-iadc    ;;;uncomment -iadc if realtime audio input is needed too
    ; For Non-realtime ouput leave only the line below:
    ; -o gen03.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    sr = 44100
    ksmps = 32
    nchnls = 2
    0dbfs  = 1
    ;example by Russell Pinkston - Univ. of Texas  (but slightly modified)

    gisine   ftgen 1, 0, 16384, 10, 1						;sine wave

    instr   1

    ihertz = cpspch(p4)
    ipkamp = p5
    iwsfn  = p6									;waveshaping function
    inmfn  = p7									;normalization function
    aenv    linen  1, .01, p3, .1        						;overall amp envelope
    actrl   linen  1, 2, p3, 2							;waveshaping index control
    aindex  poscil actrl/2, ihertz, gisine						;sine wave to be distorted
    asignal tablei .5+aindex, iwsfn, 1						;waveshaping
    anormal tablei actrl, inmfn,1							;amplitude normalization
    asig    =      asignal*anormal*ipkamp*aenv
    asig    dcblock2  asig								;get rid of possible DC
            outs   asig, asig

    endin
    </CsInstruments>
    <CsScore>
    ; first four notes are specific Chebyshev polynomials using gen03. The values were obtained from Dodge page 147

    f4 0 513 3 -1 1 0 1			; First-order Chebyshev: x
    f5 0 257 4 4 1				; Normalizing function for fn4

    f6 0 513 3 -1 1 -1 0 2			; Second-order Chebyshev: 2x2 - 1
    f7 0 257 4 6 1				; Normalizing function for fn6

    f8 0 513 3 -1 1 0 -3 0 4		; Third-order Chebyshev: 4x3 - 3x
    f9 0 257 4 8 1				; Normalizing function for fn8

    f10 0 513 3 -1 10 0 -7 0 56 0 -112 0 64	; Seventh-order Chebyshev: 64x7 - 112x5 + 56x3 - 7x
    f11 0 257 4 10 1			; Normalizing function for fn10

    f12 0 513 3 -1 1 5 4 3 2 2 1		; a 4th order polynomial function over the x-interval -1 to 1
    f13 0 257 4 12 1			; Normalizing function for fn12

    ; five notes with same fundamental, different waveshape & normalizing functions
    ;        pch	 amp	wsfn	nmfn
    i1 0  3 8.00     .7      4	 5
    i1 +  .  .	 .	 6	 7
    i1 +  .  .	 .	 8	 9
    i1 +  .  .       .	 10	 11
    i1 +  .  .       .	 12	 13

    e
    </CsScore>
    </CsoundSynthesizer>

These are the diagrams of the waveforms of the GEN03 routines, as used in the example:

f4 0 513 3 1 1 0 1 - first-order Chebyshev: x

f6 0 513 3 -1 1 -1 0 2 - second-order Chebyshev: 2x2 - 1

f8 0 513 3 -1 1 0 -3 0 4 - third-order Chebyshev: 4x3 - 3x

f10 0 513 3 -1 10 0 -7 0 56 0 -112 0 64 - seventh-order Chebyshev: 64x7 - 112x5 + 56x3 - 7x

f12 0 513 3 -1 1 5 4 3 2 2 1 - a 4th order polynomial function over the x-interval -1 to 1

## See Also

GEN13, GEN14, and GEN15.

Information about the Chebyshev polynomials on Wikipedia: http://en.wikipedia.org/wiki/Chebyshev_polynomials

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