Convert prediction filter polynomial to reflection coefficients
k = poly2rc(a)
[k,r0] = poly2rc(a,efinal)
k = poly2rc(a) converts the prediction filter polynomial a to the reflection coefficients of the corresponding lattice structure. a can be real or complex, and a(1) cannot be 0. If a(1) is not equal to 1, poly2rc normalizes the prediction filter polynomial by a(1). k is a row vector of size length(a)-1.
Given a prediction filter polynomial, a, and a final prediction error, efinal, determine the reflection coefficients of the corresponding lattice structure and the zero-lag autocorrelation.
a = [1.0000 0.6149 0.9899 0.0000 0.0031 -0.0082]; efinal = 0.2; [k,r0] = poly2rc(a,efinal)
k = 0.3090 0.9801 0.0031 0.0081 -0.0082 r0 = 5.6032
If abs(k(i)) == 1 for any i, finding the reflection coefficients is an ill-conditioned problem. poly2rc returns some NaNs and provides a warning message in those cases.
poly2rc implements this recursive relationship:
This relationship is based on Levinson's recursion . To implement it, poly2rc loops through a in reverse order after discarding its first element. For each loop iteration i, the function: