From b409a4b0c6131e01fc5a03c0fc31caa4829b0dec Mon Sep 17 00:00:00 2001
From: Johnathan Corgan <jcorgan@corganenterprises.com>
Date: Mon, 18 Jul 2011 15:54:43 -0700
Subject: gr-vocoder: re-implemented gr-codec2-vocoder inside gr-vocoder
---
gr-vocoder/lib/codec2/lsp.c | 325 ++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 325 insertions(+)
create mode 100644 gr-vocoder/lib/codec2/lsp.c
(limited to 'gr-vocoder/lib/codec2/lsp.c')
diff --git a/gr-vocoder/lib/codec2/lsp.c b/gr-vocoder/lib/codec2/lsp.c
new file mode 100644
index 0000000000..47001c1efd
--- /dev/null
+++ b/gr-vocoder/lib/codec2/lsp.c
@@ -0,0 +1,325 @@
+/*---------------------------------------------------------------------------*\
+
+ FILE........: lsp.c
+ AUTHOR......: David Rowe
+ DATE CREATED: 24/2/93
+
+
+ This file contains functions for LPC to LSP conversion and LSP to
+ LPC conversion. Note that the LSP coefficients are not in radians
+ format but in the x domain of the unit circle.
+
+\*---------------------------------------------------------------------------*/
+
+/*
+ Copyright (C) 2009 David Rowe
+
+ All rights reserved.
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU Lesser General Public License version 2.1, as
+ published by the Free Software Foundation. This program is
+ distributed in the hope that it will be useful, but WITHOUT ANY
+ WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+ License for more details.
+
+ You should have received a copy of the GNU Lesser General Public License
+ along with this program; if not, see <http://www.gnu.org/licenses/>.
+*/
+
+#include "defines.h"
+#include "lsp.h"
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+/* Only 10 gets used, so far. */
+#define LSP_MAX_ORDER 20
+
+/*---------------------------------------------------------------------------*\
+
+ Introduction to Line Spectrum Pairs (LSPs)
+ ------------------------------------------
+
+ LSPs are used to encode the LPC filter coefficients {ak} for
+ transmission over the channel. LSPs have several properties (like
+ less sensitivity to quantisation noise) that make them superior to
+ direct quantisation of {ak}.
+
+ A(z) is a polynomial of order lpcrdr with {ak} as the coefficients.
+
+ A(z) is transformed to P(z) and Q(z) (using a substitution and some
+ algebra), to obtain something like:
+
+ A(z) = 0.5[P(z)(z+z^-1) + Q(z)(z-z^-1)] (1)
+
+ As you can imagine A(z) has complex zeros all over the z-plane. P(z)
+ and Q(z) have the very neat property of only having zeros _on_ the
+ unit circle. So to find them we take a test point z=exp(jw) and
+ evaluate P (exp(jw)) and Q(exp(jw)) using a grid of points between 0
+ and pi.
+
+ The zeros (roots) of P(z) also happen to alternate, which is why we
+ swap coefficients as we find roots. So the process of finding the
+ LSP frequencies is basically finding the roots of 5th order
+ polynomials.
+
+ The root so P(z) and Q(z) occur in symmetrical pairs at +/-w, hence
+ the name Line Spectrum Pairs (LSPs).
+
+ To convert back to ak we just evaluate (1), "clocking" an impulse
+ thru it lpcrdr times gives us the impulse response of A(z) which is
+ {ak}.
+
+\*---------------------------------------------------------------------------*/
+
+/*---------------------------------------------------------------------------*\
+
+ FUNCTION....: cheb_poly_eva()
+ AUTHOR......: David Rowe
+ DATE CREATED: 24/2/93
+
+ This function evalutes a series of chebyshev polynomials
+
+ FIXME: performing memory allocation at run time is very inefficient,
+ replace with stack variables of MAX_P size.
+
+\*---------------------------------------------------------------------------*/
+
+
+static float
+cheb_poly_eva(float *coef,float x,int m)
+/* float coef[] coefficients of the polynomial to be evaluated */
+/* float x the point where polynomial is to be evaluated */
+/* int m order of the polynomial */
+{
+ int i;
+ float *t,*u,*v,sum;
+ float T[(LSP_MAX_ORDER / 2) + 1];
+
+ /* Initialise pointers */
+
+ t = T; /* T[i-2] */
+ *t++ = 1.0;
+ u = t--; /* T[i-1] */
+ *u++ = x;
+ v = u--; /* T[i] */
+
+ /* Evaluate chebyshev series formulation using iterative approach */
+
+ for(i=2;i<=m/2;i++)
+ *v++ = (2*x)*(*u++) - *t++; /* T[i] = 2*x*T[i-1] - T[i-2] */
+
+ sum=0.0; /* initialise sum to zero */
+ t = T; /* reset pointer */
+
+ /* Evaluate polynomial and return value also free memory space */
+
+ for(i=0;i<=m/2;i++)
+ sum+=coef[(m/2)-i]**t++;
+
+ return sum;
+}
+
+
+/*---------------------------------------------------------------------------*\
+
+ FUNCTION....: lpc_to_lsp()
+ AUTHOR......: David Rowe
+ DATE CREATED: 24/2/93
+
+ This function converts LPC coefficients to LSP coefficients.
+
+\*---------------------------------------------------------------------------*/
+
+int lpc_to_lsp (float *a, int lpcrdr, float *freq, int nb, float delta)
+/* float *a lpc coefficients */
+/* int lpcrdr order of LPC coefficients (10) */
+/* float *freq LSP frequencies in radians */
+/* int nb number of sub-intervals (4) */
+/* float delta grid spacing interval (0.02) */
+{
+ float psuml,psumr,psumm,temp_xr,xl,xr,xm = 0;
+ float temp_psumr;
+ int i,j,m,flag,k;
+ float *px; /* ptrs of respective P'(z) & Q'(z) */
+ float *qx;
+ float *p;
+ float *q;
+ float *pt; /* ptr used for cheb_poly_eval()
+ whether P' or Q' */
+ int roots=0; /* number of roots found */
+ float Q[LSP_MAX_ORDER + 1];
+ float P[LSP_MAX_ORDER + 1];
+
+ flag = 1;
+ m = lpcrdr/2; /* order of P'(z) & Q'(z) polynimials */
+
+ /* Allocate memory space for polynomials */
+
+ /* determine P'(z)'s and Q'(z)'s coefficients where
+ P'(z) = P(z)/(1 + z^(-1)) and Q'(z) = Q(z)/(1-z^(-1)) */
+
+ px = P; /* initilaise ptrs */
+ qx = Q;
+ p = px;
+ q = qx;
+ *px++ = 1.0;
+ *qx++ = 1.0;
+ for(i=1;i<=m;i++){
+ *px++ = a[i]+a[lpcrdr+1-i]-*p++;
+ *qx++ = a[i]-a[lpcrdr+1-i]+*q++;
+ }
+ px = P;
+ qx = Q;
+ for(i=0;i<m;i++){
+ *px = 2**px;
+ *qx = 2**qx;
+ px++;
+ qx++;
+ }
+ px = P; /* re-initialise ptrs */
+ qx = Q;
+
+ /* Search for a zero in P'(z) polynomial first and then alternate to Q'(z).
+ Keep alternating between the two polynomials as each zero is found */
+
+ xr = 0; /* initialise xr to zero */
+ xl = 1.0; /* start at point xl = 1 */
+
+
+ for(j=0;j<lpcrdr;j++){
+ if(j%2) /* determines whether P' or Q' is eval. */
+ pt = qx;
+ else
+ pt = px;
+
+ psuml = cheb_poly_eva(pt,xl,lpcrdr); /* evals poly. at xl */
+ flag = 1;
+ while(flag && (xr >= -1.0)){
+ xr = xl - delta ; /* interval spacing */
+ psumr = cheb_poly_eva(pt,xr,lpcrdr);/* poly(xl-delta_x) */
+ temp_psumr = psumr;
+ temp_xr = xr;
+
+ /* if no sign change increment xr and re-evaluate
+ poly(xr). Repeat til sign change. if a sign change has
+ occurred the interval is bisected and then checked again
+ for a sign change which determines in which interval the
+ zero lies in. If there is no sign change between poly(xm)
+ and poly(xl) set interval between xm and xr else set
+ interval between xl and xr and repeat till root is located
+ within the specified limits */
+
+ if((psumr*psuml)<0.0){
+ roots++;
+
+ psumm=psuml;
+ for(k=0;k<=nb;k++){
+ xm = (xl+xr)/2; /* bisect the interval */
+ psumm=cheb_poly_eva(pt,xm,lpcrdr);
+ if(psumm*psuml>0.){
+ psuml=psumm;
+ xl=xm;
+ }
+ else{
+ psumr=psumm;
+ xr=xm;
+ }
+ }
+
+ /* once zero is found, reset initial interval to xr */
+ freq[j] = (xm);
+ xl = xm;
+ flag = 0; /* reset flag for next search */
+ }
+ else{
+ psuml=temp_psumr;
+ xl=temp_xr;
+ }
+ }
+ }
+
+ /* convert from x domain to radians */
+
+ for(i=0; i<lpcrdr; i++) {
+ freq[i] = acos(freq[i]);
+ }
+
+ return(roots);
+}
+
+/*---------------------------------------------------------------------------*\
+
+ FUNCTION....: lsp_to_lpc()
+ AUTHOR......: David Rowe
+ DATE CREATED: 24/2/93
+
+ This function converts LSP coefficients to LPC coefficients. In the
+ Speex code we worked out a way to simplify this significantly.
+
+\*---------------------------------------------------------------------------*/
+
+void lsp_to_lpc(float *lsp, float *ak, int lpcrdr)
+/* float *freq array of LSP frequencies in radians */
+/* float *ak array of LPC coefficients */
+/* int lpcrdr order of LPC coefficients */
+
+
+{
+ int i,j;
+ float xout1,xout2,xin1,xin2;
+ float *pw,*n1,*n2,*n3,*n4 = 0;
+ int m = lpcrdr/2;
+ float freq[LSP_MAX_ORDER];
+ float Wp[(LSP_MAX_ORDER * 4) + 2];
+
+ /* convert from radians to the x=cos(w) domain */
+
+ for(i=0; i<lpcrdr; i++)
+ freq[i] = cos(lsp[i]);
+
+ pw = Wp;
+
+ /* initialise contents of array */
+
+ for(i=0;i<=4*m+1;i++){ /* set contents of buffer to 0 */
+ *pw++ = 0.0;
+ }
+
+ /* Set pointers up */
+
+ pw = Wp;
+ xin1 = 1.0;
+ xin2 = 1.0;
+
+ /* reconstruct P(z) and Q(z) by cascading second order polynomials
+ in form 1 - 2xz(-1) +z(-2), where x is the LSP coefficient */
+
+ for(j=0;j<=lpcrdr;j++){
+ for(i=0;i<m;i++){
+ n1 = pw+(i*4);
+ n2 = n1 + 1;
+ n3 = n2 + 1;
+ n4 = n3 + 1;
+ xout1 = xin1 - 2*(freq[2*i]) * *n1 + *n2;
+ xout2 = xin2 - 2*(freq[2*i+1]) * *n3 + *n4;
+ *n2 = *n1;
+ *n4 = *n3;
+ *n1 = xin1;
+ *n3 = xin2;
+ xin1 = xout1;
+ xin2 = xout2;
+ }
+ xout1 = xin1 + *(n4+1);
+ xout2 = xin2 - *(n4+2);
+ ak[j] = (xout1 + xout2)*0.5;
+ *(n4+1) = xin1;
+ *(n4+2) = xin2;
+
+ xin1 = 0.0;
+ xin2 = 0.0;
+ }
+}
+
--
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