**GEN** Routines: Amplitude Scaling

## GEN12

**f** # time size -12 xint

### Description

This generates the log of a modified Bessel function of the second kind, order 0, suitable for use in amplitude-modulated FM.

### Initialization

*size * – number of points in the table. Must be a power of 2 or a power-of-2 plus 1 (see **f statement**). The normal value is power-of-2 plus 1.

*xint* – specifies the *x* interval [0 to *+xint*] over which the function is defined.

### Note

This subroutine draws the natural log of a modified Bessel function of the second kind, order 0 (commonly written as **I** subscript 0), over the x-interval requested. The call should have rescaling inhibited.

The function is useful as an amplitude scaling factor in cycle-synchronous amplitude-modulated FM. (See Palamin & Palamin, *J. Audio Eng. Soc., 36/9*, Sept. 1988, pp.671-684.) The algorithm is interesting because it permits the normally symmetric FM spectrum to be made asymmetric around a frequency other than the carrier, and is thereby useful for formant positioning. By using a table lookup index of **I**(r - 1/r), where **I** is the FM modulation index and **r** is an exponential parameter affecting partial strengths, the Palamin algorithm becomes relatively efficient, requiring only oscil's, table lookups, and a single **exp** call.

### Example

**f** 1 0 2049 -12 20

This draws an unscaled *ln(I0(x))* from 0 to 20.

**GEN** Routines: Amplitude Scaling