Source: audio_blocks/include/lpc.h

/*
Copyright 1992, 1993, 1994 by Jutta Degener and Carsten Bormann,
Technische Universitaet Berlin

Any use of this software is permitted provided that this notice is not
removed and that neither the authors nor the Technische Universitaet Berlin
are deemed to have made any representations as to the suitability of this
software for any purpose nor are held responsible for any defects of
this software.  THERE IS ABSOLUTELY NO WARRANTY FOR THIS SOFTWARE.

As a matter of courtesy, the authors request to be informed about uses
this software has found, about bugs in this software, and about any
improvements that may be of general interest.

Berlin, 28.11.1994
Jutta Degener
Carsten Bormann
*/


/* LPC- and Reflection Coefficients
 *
 * The next two functions calculate linear prediction coefficients
 * and/or the related reflection coefficients from the first P_MAX+1
 * values of the autocorrelation function.
 */

/* Invented by N. Levinson in 1947, modified by J. Durbin in 1959.
 */
inline float                      /* returns minimum mean square error    */
wld(
        float       * lpc, /*      [0...p-1] LPC coefficients      */
        const float * ac,  /*  in: [0...p] autocorrelation values  */
        float       * ref, /* out: [0...p-1] reflection coef's     */
        int p
        )
{
        int i, j;  float r, error = ac[0];

        lpc[0]=1; //for compatibility
        lpc++; //for compatibility

        if (ac[0] == 0) {
                for (i = 0; i < p; i++) ref[i] = 0; return 0; }

        for (i = 0; i < p; i++) {

                /* Sum up this iteration's reflection coefficient.
                 */
                r = -ac[i + 1];
                for (j = 0; j < i; j++) r -= lpc[j] * ac[i - j];
                ref[i] = r /= error;

                /*  Update LPC coefficients and total error.
                 */
                lpc[i] = r;
                for (j = 0; j < i/2; j++) {
                        float tmp  = lpc[j];
                        lpc[j]     += r * lpc[i-1-j];
                        lpc[i-1-j] += r * tmp;
                }
                if (i % 2) lpc[j] += lpc[j] * r;

                error *= 1.0 - r * r;
        }
        return error;
}


/* Compute the autocorrelation
 *                      ,--,
 *              ac(i) = >  x(n) * x(n-i)  for all n
 *                      `--'
 * for lags between 0 and lag-1, and x == 0 outside 0...n-1
 */
inline void autocorr(
        const float * x,   /*  in: [0...n-1] samples x   */
        float *ac,   /* out: [0...lag-1] ac values */
        int lag, int   n)
{
        float d; int i;
        lag++;   //Conpensate for the old routine
        while (lag--) {
                for (i = lag, d = 0; i < n; i++) d += x[i] * x[i-lag];
                ac[lag] = d;
        }
}