This subroutine generates a stored function table by evaluating a polynomial in x over a fixed interval and with specified coefficients.
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.
Here is a simple example of the GEN03 routine. It uses the files gen03.orc and gen03.sco. It fills a table with a 4th order polynomial function over the x-interval -1 to 1. The origin will be at the offset position 512. The function is post-normalized. Here is its diagram:
Diagram of the waveform generated by GEN03.
Example 16-1. A simple example of the GEN03 routine.
/* gen03.orc */
; Initialize the global variables.
sr = 44100
kr = 4410
ksmps = 10
nchnls = 1
; Instrument #1.
instr 1
; Create an index over the length of our entire note.
kcps init 1/p3
kndx phasor kcps
; Read Table #1 with our index.
ifn = 1
ixmode = 1
kamp table kndx, ifn, ixmode
; Create a sine wave, use the Table #1 values to control
; the amplitude.
a1 oscil kamp*30000, 440, 2
out a1
endin
/* gen03.orc */
/* gen03.sco */
; Table #1: a polynomial function (using GEN03).
f 1 0 1025 3 -1 1 5 4 3 2 2 1
; Table #2, a sine wave.
f 2 0 16384 10 1
; Play Instrument #1 for 2 seconds.
i 1 0 2
e
/* gen03.sco */