lpc

Compute the linear prediction coefficients using the autocorrelation method ("Linear Prediction of Speech", Markel & Gray).

Usage

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

xthe 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

pdifferentiation 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

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

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).

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