Dear All,
Is there a script or function somewhere which calculates the Linear
prediction model (LPC) of a signal frame?
I tried to implement a function (below) without using the algorithm of
Levinson & Durbin but it doesn't seem to work properly. seemingly the
problem is due to inaccuracy of the matrix equation solution.
Regards,
Federico Miyara
function a=lpc(x, p)
// Calculation of the LPC coeficients
// Usage:
// a = lpc(x, p)
// where
// x: Signal vector
// p: Order of the linear prediction model
// a: Coefficients of the linear prediction model
//
// The coefficients are computed so to get minimize the
// prediction error by the least-square method
//
// ------------------------------
// Author: Federico Miyara
// Date: 20202-09-27
if 1==2
// Test data --delete--
// LPC order
p = 10
// Signal length
N = 512
// Create whiter noise
exec whitenoise.sci;
y = whitenoise(2*N-1,1);
// Create a filter
// Create some poles within the unit circle for stability
pol = 0.7 + %i*linspace(-0.3,0.3,10)
// Denominator polynomial in z
AAA = real(prod(%z - pol))
// Theoretical LPC coefficients
aa = -coeff(AAA)($-1:-1:1)
// Autorregressive (AR) transfer function
HH = 1/(1 - sum(aa.*%z^(-(1:p))))
// Numerator and denominator
BB = HH.num
AA = HH.den
// Filter white noise
x = filter(BB, AA, y);
x = x(N+1:2*N);
plot(x)
end
for h = 1:p
// Row h
for i = 1:p
// Column i
A(h,i) = sum(x(p+1-i:$-i).*x(p+1-h:$-h));
end
B(h) = sum(x(p+1:$).*x(p+1-h:$-h));
end
a = ((inv(A)*B))';
if 1==2
H = 1/(1 - sum(a.*%z^(-(1:p))))
// Numerator and denominator
B1 = H.num
A1 = H.den
// Filter white noise
x1 = filter(B1, A1, y);
x1 = x1(N+1:2*N);
plot(x1)
end
endfunction
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