Programmer Guide/Command Reference/EVAL/lpc: Difference between revisions

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=====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:<code>lpc(<var>x</var>, <var>m</var>, <var>p</var> {, <var>type</var> {, <var>lfft</var>}})</code>
:;<var>x</var>:the signal vector; this should be a speech signal without windowing function (because the hamming-window is applied to ''x'' by this function)
:;<var>m</var>:number of coefficients
::rule of thumb: ''m'' ~ samplingrate / 1000 * 1.25
:;<var>p</var>:differentiation factor; 0 &le; ''p'' &le; 1 (default=0)
:;<var>type</var>:output selector; 0 &le; ''type'' &le; 4 (default=0)
:;<var>lfft</var>: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:
# apply differentiation to signal ''x''
# apply hamming window to signal ''x''
# use the autocorelation method to compute the inverse filter coefficients ''ai'', the reflection coefficients ''rc'' and the error (or residual) energy ''alpha''
# convert coefficients to the selected result
;Result:A vector ''y'' containing the result of the function.
:{|class="einrahmen"
!''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'''
|<code>''y''[0]=''alpha''</code><BR><code>''y''[1..M+1]=''ai[0..''m'']</code>
|''m''+2
|the error energy (''alpha'') and the ''m''+1 inverse filter coefficients ''ai''
|-
|'''2'''
|<code>''y''[0]=''alpha''</code><BR><code>''y''[1..M]=''rc[0..''m''-1]</code>
|''m''+1
|the error energy (''alpha'') and the ''m'' reflection coefficients ''rc''
|-
|'''3'''
|<code>''y''[0]=''alpha''</code><BR><code>''y''[1..M+1]=''ar[0..''m'']</code>
|''m''+2
|the error energy (''alpha'') and the ''m'' area coefficients ''ar''<BR>(''ar''[i] ~ area of section i)
|-
|'''4'''
|<code>''y''[0]=''alpha''</code><BR><code>''y''[1..M+1]=''lar[0..''m'']</code>
|''m''+2
|the error energy (''alpha'') and the ''m'' log. area coefficients ''lar''<BR>(''lar''[i] ~ diameter of section i)
|}
;See also: [[../fft|fft]], [[../ifft|ifft]], [[../dft|dft]], [[../dct|dct]], [[../cepstrum|cepstrum]]


Compute the linear prediction coefficients using a Hamming window.
[[../#Functions|<function list>]]
 
=====Usage:=====
 
<code>lpc(<var>x</var>, <var>m</var>, <var>p</var> {, <var>out</var>, <var>lfft</var>})</code>
 
=====Function:=====
 
Computes the linear prediction coefficients or the lpc smoothed spectrum of the signal vector x using the auto-correlation method.
 
=====Parameters:=====
 
;<var>x</var>
 
:An unwindowed signal vector.
 
;<var>m</var>
 
:The number of coefficients.
 
;<var>p</var>
 
:The pre-emphasis factor (<code>0 <=</code> <var>p</var> <code><= 1</code>).
 
;<var>out</var>
 
:The output selector. See the result for details.
 
;<var>lfft</var>
 
:The fft length for smoothed spectrum.
 
=====Result:=====
 
A vector <code>y</code>. The type of vector depends on the parameter <var>out</var>:
 
<code>0</code> - A smoothed linear amplitude spectrum where <code>length =</code> <var>lfft</var><code>/2+1</code> and <code>y[0 ..</code> <var>lfft</var><code>/2]</code>.
 
<code>1</code> - The error energy and inverse filter coefficients where <code>length =</code> <var>m</var><code>+2</code> and <code>y[0] = alpha</code> and <code>y[1 ..</code> <var>m</var><code>+1] = AI[0..</code><var>m</var><code>]</code>.
 
<code>2</code> - The error energy and reflection coefficients where <code>length =</code> <var>m</var><code>+1</code>, <code>y[0] = alpha</code> and <code>y[1..</code><var>m</var><code>] = RC[0..</code><var>m</var><code>-1]</code>.
 
<code>3</code> - The error energy and area coefficients where <code>length =</code> <var>m</var><code>+1</code>, <code>y[0] = alpha</code> and <code>y[1..</code><var>m</var><code>] = AR[0..</code><var>m</var><code>-1]</code>.
 
<code>4</code> - The error energy and log. area coefficients where <code>length =</code> <var>m</var><code>+1</code>, <code>y[0] = alpha</code> and <code>y[1..</code><var>m</var><code>] = sqrt(AR[0..</code><var>m</var><code>-1])</code>.

Latest revision as of 09:11, 2 May 2018

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 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

<function list>

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