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

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=====cepstrum=====
Compute the real cepstrum or the cepstrum smoothed/liftered spectrum of the logarithmic spectrum ''x''.
----
;Usage 1:<code>cepstrum(<var>x</var>)</code>
:;<var>x</var>: a vector containing a log. amplitude spectrum
::*note: because a radix-2 fft/ifft is used for the computation, the spectrum stored in ''x'' must be computed from a signal with <code>L=2^M</code> samples (<code>&rarr; nrow(''x'')=L/2+1=2^M/2+1</code>).
;Result 1:A vector with <code>L/2</code> values, containing the coefficients or the real cepstrum of ''x''.
----
;Usage 2:<code>cepstrum(<var>x</var>, <var>m</var>)</code>
:;<var>x</var>: a vector containing a log. amplitude spectrum
:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' &le; L/2
;Description:
:# The real cepstrum ''c'' of ''x'' is computed.
:# The coefficents ''m'' to <code>L/2-1</code> of the cepstrum ''c'' are set to zero.
:# The smoothed spectrum is computed from the modified cepstrum ''c''.
;Result 2:A vector with same length as ''x'', containing the smoothed spectrum.
----
;Usage 2:<code>cepstrum(<var>x</var>, <var>o</var>, <var>m</var>)</code>
:;<var>x</var>: a vector containing a log. amplitude spectrum
:;<var>o</var>: the first coefficient to be used for smoothing; 0 < ''o'' < L/2
:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' &le; L/2-''o''
;Description:
:# The real cepstrum ''c'' of ''x'' is computed.
:# The coefficents 0 to ''o''-1 and ''o''+''m'' to <code>L/2-1</code> of the cepstrum ''c'' are set to zero.
:# The liftered spectrum is computed from the modified cepstrum ''c''.
;Result 2:A vector with same length as ''x'', containing the liftered spectrum.
----
;See also: [[../fft|fft]], [[../ifft|ifft]], [[../dft|dft]], [[../dct|dct]], [[../lpc|lpc]], [[../ipeak|ipeak]], [[../formants|formants]]


Cepstrum.
[[../#Functions|<function list>]]
 
=====Usage:=====
 
<code>cepstrum(<var>x</var>)</code>
 
=====Function:=====
 
Computes the real cepstrum of <var>x</var>.
 
=====Result:=====
 
A vector containing the cepstrum coefficients.
 
=====Usage:=====
 
<code>cepstrum(<var>x</var>, <var>n</var>)</code>
 
=====Function:=====
 
Computes the cepstrum smoothed spectrum of <var>x</var> using the first <var>n</var> coefficients.
 
=====Result:=====
 
The cepstrum smoothed spectrum. This is the same type as <var>x</var>.
 
=====Usage:=====
 
<code>cepstrum(<var>x</var>, <var>o</var>, <var>n</var>)</code>
 
=====Function:=====
 
Computes the cepstrum smoothed spectrum of <var>x</var> using the coefficients o to <var>o</var><code>+</code><var>n</var><code>-1</code>.
 
=====Result:=====
 
The cepstrum smoothed spectrum. This is the same type as <var>x</var>.
 
=====Notes:=====
 
<var>x</var> must be a log. amplitude spectrum computed with a radix-2 fft.

Latest revision as of 19:26, 21 April 2011

Compute the real cepstrum or the cepstrum smoothed/liftered spectrum of the logarithmic spectrum x.

Usage 1
cepstrum(x)
x
a vector containing a log. amplitude spectrum
  • note: because a radix-2 fft/ifft is used for the computation, the spectrum stored in x must be computed from a signal with L=2^M samples (→ nrow(x)=L/2+1=2^M/2+1).
Result 1
A vector with L/2 values, containing the coefficients or the real cepstrum of x.
Usage 2
cepstrum(x, m)
x
a vector containing a log. amplitude spectrum
m
the number of coefficients to be used for smoothing; 0 < m ≤ L/2
Description
  1. The real cepstrum c of x is computed.
  2. The coefficents m to L/2-1 of the cepstrum c are set to zero.
  3. The smoothed spectrum is computed from the modified cepstrum c.
Result 2
A vector with same length as x, containing the smoothed spectrum.
Usage 2
cepstrum(x, o, m)
x
a vector containing a log. amplitude spectrum
o
the first coefficient to be used for smoothing; 0 < o < L/2
m
the number of coefficients to be used for smoothing; 0 < m ≤ L/2-o
Description
  1. The real cepstrum c of x is computed.
  2. The coefficents 0 to o-1 and o+m to L/2-1 of the cepstrum c are set to zero.
  3. The liftered spectrum is computed from the modified cepstrum c.
Result 2
A vector with same length as x, containing the liftered spectrum.
See also
fft, ifft, dft, dct, lpc, ipeak, formants

<function list>

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