LPC - Linear Predictive Coding

lpc(x::AbstractVector, p::Integer, [LPCBurg()])

Given input signal x and prediction order p, returns IIR coefficients a and average reconstruction error prediction_err. Note that this method does NOT return the leading $1$ present in the true autocorrelative estimate; it omits it as it is implicit in every LPC estimate, and must be manually reintroduced if the returned vector should be treated as a polynomial.

The algorithm used is determined by the last optional parameter, and can be either LPCBurg (arburg) or LPCLevinson (levinson).

arburg(x::AbstractVector, p::Integer)

LPC (Linear Predictive Coding) estimation, using the Burg method. This function implements the mathematics published in ^[Lagrange], and the recursion relation as noted in ^[Vos], in turn referenced from ^[Andersen].

levinson(x::AbstractVector, p::Integer)

Implements Levinson recursion, as described in ^[Levinson], to find the solution a of the linear equation

\[\mathbf{T} (-\vec{a}) = \begin{bmatrix} x_2 \\ \vdots \\ x_{p+1} \end{bmatrix}\]

in the case where $\mathbf{T}$ is Hermitian and Toeplitz, with first column x[1:p]. This function can be used for LPC (Linear Predictive Coding) estimation, by providing LPCLevinson() as an argument to lpc.