lpc

Compute the linear prediction coefficients using the autocorrelation method. This function implements an all-pole filter approximation of the acoustic tube modell of the vocal tract. The implementation is based on the book "Linear Prediction of Speech" (J.D. Markel & A.H. Gray, Springer 1976).

Usage

lpc(x, m, p {, type {, lfft}})

x

the signal vector; this should be a speech signal without windowing function (because the hamming-window is applied to x by this the function)

m

number of coefficients

rule of thumb: m ~ samplingrate / 1000 * 1.25

p

differentiation factor; 0 <= p <= 1 (default=0)

type

output selector; 0 <= type <= 4 (default=0)

lfft

the length of the fft to be used for the computation of the transfer function (amplitude spectrum) of the inverse filter; m+1 < lfft

note: if necessary, the value of lfft is automatically corrected to the next possible value

Description

1. apply differentiation to signal x
2. apply hamming window to signal x
3. use the autocorelation method to compute the inverse filter coefficients ai, the reflection coefficients rc and the error (or residual) energy alpha
4. convert coefficients to the selected result

Result

A vector y containing the result of the function.

type	y	nrow(y)	description
0	amplitude spectrum of the inverse filter	lfft/2+1	this function can be used in speech analysis to compute the transfer function of the vocal tract (e.g. for formant extraction)
1	y[0]=alpha y[1..M+1]=ai[0..m]	m+2	the error energy (alpha) and the m+1 inverse filter coefficients ai
2	y[0]=alpha y[1..M]=rc[0..m-1]	m+1	the error energy (alpha) and the m reflection coefficients rc
3	y[0]=alpha y[1..M+1]=ar[0..m]	m+2	the error energy (alpha) and the m area coefficients ar (ar[i] ~ area of section i)
4	y[0]=alpha y[1..M+1]=lar[0..m]	m+2	the error energy (alpha) and the m log. area coefficients lar (lar[i] ~ diameter of section i)

See also

fft, ifft, dft, dct, cepstrum, complex arithmetic