Modified covariance method (a.k.a forward-backward method) of LPC calculation

armcov.jl

function armcov(x,L)
    N = length(x)
    phi = zeros(L+1,L+1)
    for k = 0:L, i=0:L, n=0:N-L-1
        phi[k+1,i+1] += x[n+1+k]*x[n+1+i] + x[n+1+L-k]*x[n+1+L-i]
    end
    phi = phi./(2*(N-L))

    a = phi[2:end,2:end]\-phi[2:end,1]
    P = phi[1,1] + phi[1,2:end]*a

    [1,a],P
end

x =[1:10,10:-1:1]
a,P = armcov(x,5)
print(a)
print(P)