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+/*
+ 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
+
+
+ Code slightly modified by Jean-Marc Valin
+
+ Speex License:
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+
+ - Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ - Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ - Neither the name of the Xiph.org Foundation nor the names of its
+ contributors may be used to endorse or promote products derived from
+ this software without specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
+ CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+
+
+/* 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.
+ */
+
+#include "lpc.h"
+
+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];
+
+ 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
+ */
+void _spx_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;
+ while (lag--) {
+ for (i = lag, d = 0; i < n; i++) d += x[i] * x[i-lag];
+ ac[lag] = d;
+ }
+}