**GEN** Routines: Waveshaping

## GEN03

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

### Description

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

### 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**.

### Example

**f** 1 0 1025 3 -1 1 5 4 3 2 2 1

This calls **GEN03** to fill 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.

**GEN** Routines: Waveshaping