线性预测与Levinson-Durbin算法实现

在学习信号处理的时候，线性预测是一个比较难理解的知识点，为了加快很多朋友的理解，这里给出Levinson-Durbin算法的线性预测实现和一个测试Demo，Demo中很明确的把输入信号、预测信号、预测误差打印了出来，这样就能以最直观的方式，把线性预测的实现与作用展示出来。话不多说，直接上代码！

typedef float　OsFlt32;
typedef int　　OsInt32;

OsFlt32 lpc(const OsFlt32 *r,OsInt32 p,OsFlt32 *a)
{
OsInt32 i,j;
OsFlt32 err;

if(0 == r[0])
{
for(i = 0; i < p; i++) a[i] = 0;
return 0;
}
a[0] = 1.0;
err = r[0];
for(i = 0; i < p; i++)
{
OsFlt32 lambda = 0.0;
for(j = 0; j <= i; j++)
lambda -= a[j]*r[i+1-j];
lambda /= err;
// Update LPC coefficients and total error
for(j = 0; j <= (i+1)/2; j++)
{
OsFlt32 temp = a[i+1-j] + lambda * a[j];
a[j] = a[j] + lambda * a[i+1-j];
a[i+1-j] = temp;
}
err *= (1.0 - lambda*lambda);
}
return err;
}

void autocorr(const OsFlt32 *x,OsInt32 n,OsFlt32 *r,OsInt32 k)
{
OsFlt32 d;
OsInt32 i,p;

for(p = 0; p <= k; p++)
{
for(i = 0,d = 0.0; i < n-p; i++)
d += x[i] * x[i+p];
r[p] = d;
}
}

#include "lpc.h"

int main(int argc,char **argv)
{
OsInt32 nLen = 128;
OsFlt32 *pOriginal,*pPredicted;
OsInt32 i,j;
const OsInt32 order = 4;
OsFlt32 R[order+1] = {0.0};
OsFlt32 A[order+1] = {0.0};
OsFlt32 error;

pOriginal   = (OsFlt32*)calloc(nLen,sizeof(OsFlt32));
pPredicted  = (OsFlt32*)calloc(nLen,sizeof(OsFlt32));

for(i = 0; i < nLen; i++)
pOriginal[i] = sin(i*0.01) + 0.75 * sin(i*0.03) + 0.5 * sin(i*0.05) + 0.25 * sin(i*0.11);

autocorr(pOriginal,nLen,R,order);
lpc(R,order,A);

for(i = 1; i <= order; i++)
A[i-1] = A[i];

for(i = order; i < nLen; i++)
{
pPredicted[i] = 0.0;
for(j = 0; j < order; j++)
pPredicted[i] -= A[j] * pOriginal[i-1-j];
}

error = 0;
for(i = order; i < nLen; i++)
{
double delta = pPredicted[i] - pOriginal[i];
printf( "Index: %.2d / Original: %.6f / Predicted: %.6f\n",i,pOriginal[i],pPredicted[i]);
error += delta * delta;
}
printf("Forward Linear Prediction Approximation Error: %f\n",error);

free(pPredicted);
free(pOriginal);
return 0;
}