求线性预测自相关法Levinson-Durbin算法或协方差法的C或C++实现

Syntax
r = rlevinson(a,efinal)
[r,u] = rlevinson(a,efinal)
[r,u,k] = rlevinson(a,efinal)
[r,u,k,e] = rlevinson(a,efinal)

Description
The reverse Levinson-Durbin recursion implements the step-down algorithm for solving the following symmetric Toeplitz system of linear equations for r, where r = [r(1) L r(p+1)] and r(i)* denotes the complex conjugate of r(i).

r = rlevinson(a,efinal) solves the above system of equations for r given vector a, where a = [1 a(2) L a(p+1)]. In linear prediction applications, r represents the autocorrelation sequence of the input to the prediction error filter, where r(1) is the zero-lag element. The figure below shows the typical filter of this type, where H(z) is the optimal linear predictor, x(n) is the input signal, is the predicted signal, and e(n) is the prediction error.

Input vector a represents the polynomial coefficients of this prediction error filter in descending powers of z.