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

Revision as of 13:35, 12 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 the 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

The real cepstrum c of x is computed.
The coefficents m to L/2-1 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

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

The real cepstrum c of x is computed.
The coefficents 0 to o-1 and o+m to L/2-1 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: ifft, dft, dct, cepstrum, lpc, complex arithmetic

@@ Line 4: / Line 4: @@
 ;Usage 1:<code>cepstrum(<var>x</var>)</code>
 :;<var>x</var>: a vector containing a log. amplitude spectrum
-:::*note: because the fft/ifft is used for the computation, the spectrum stored in ''x'' must be computed from a signal with <code>L=2^M</samples> (<code>-> nrow(''x'')=2^M/2+1</code>).
+::*note: because the 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>-> nrow(''x'')=L/2+1=2^M/2+1</code>).
-;Result 1:The next (nearest) possible signal window length.
+;Result 1:A vector with <code>L/2</code> values, containing the coefficients or the real cepstrum of ''x''.
 ----
-;Usage 2:<code>fft(<var>x</var>)</code>
+;Usage 2:<code>cepstrum(<var>x</var>, <var>m</var>)</code>
-:;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed
+:;<var>x</var>: a vector containing a log. amplitude spectrum
-;Result 2:A matrix ''y'' with [[../ncol|ncol(''x'')]] columns and L+2 rows, where each column ''y''[*,j] contains the complex spectrum of the column (channel) ''x''[*,j]. The transformation length L is set to [[../npow2|npow2(nrow(''x''))]].
+:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' <= 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 3:<code>fft(<var>x</var>, <var>n</var> {, <var>ytype</var>, <var>poffset</var>, <var>prange</var>, <var>aref</var>})</code>
+;Usage 2:<code>cepstrum(<var>x</var>, <var>o</var>, <var>m</var>)</code>
-:;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed
+:;<var>x</var>: a vector containing a log. amplitude spectrum
-:;<var>n</var>: desired length of analysis window;
+:;<var>o</var>: the first coefficient to be used for smoothing; 0 < ''o'' < L/2
-::*If <code>''n'' < nrow(''x'')</code>, the analysis window length L is set to nrow(''x''), otherwise L is set to ''n''.
+:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' <= L/2-''o''
-::*If the analysis window length L is a power of 2 (L=2^M), the '''fft''' algorithm is used, otherwise the '''dft''' is used.
+;Description:
-::*If L is greater than [[../nrow|nrow(''x'')]], zero padding is applied to the signal.
+:# The real cepstrum ''c'' of ''x'' is computed.
-:;<var>ytype</var>: select the type and format of the computed spectrum (default=0) -> see '''Result 3'''
+:# The coefficents 0 to ''o''-1 and ''o''+''m'' to <code>L/2-1</code> of the cepstrum ''c'' are set to zero.
-:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0)
+:# The liftered spectrum is computed from the modified cepstrum ''c''.
-:::{|class="keinrahmen"
+;Result 2:A vector with same length as ''x'', containing the liftered spectrum.
-|''poffset''='''0''' ||-> <code>phase[i] = atan2(im[i], re[i])</code>
-|-
-|otherwise ||-> <code>phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * ''poffset'') % (2 * pi)</code>
-|}
-:;<var>prange</var>: selects the range of phase values (default=0)
-:::{|class="keinrahmen"
-|''prange''='''0''' ||-> <code>0 <= phase[i] < 2*pi</code>
-|-
-|otherwise ||-> <code>-pi <= phase[i] < pi</code>
-|}
-:;<var>aref</var>: reference amplitude if the log. spectrum (''ytype''=4) is requested (default=1)
-;Result 3: A matrix ''y'' with [[../ncol|ncol(''x'')]] columns, where each column ''y''[*,j] contains the spectrum of the column (channel) ''x''[*,j]. The type and the length of the spectra is selected by the argument ''ytype''.
-::{|class="einrahmen"
-!''ytype'' !! description !! content of ''y''[*,j] !! nrow(''y'')
-|-
-|'''0'''
-|complex spectrum in cartesian format
-|<code>{ re<sub>0</sub>, im<sub>0</sub>, re<sub>1</sub>, im<sub>1</sub>, ... }</code>
-|L+2
-|-
-|'''1'''
-|complex spectrum in polar format
-|<code>{ amp<sub>0</sub>, phase<sub>0</sub>, amp<sub>1</sub>, phase<sub>1</sub>, ... }<BR>with: amp<sub>i</sub>=sqrt(re<sub>i</sub><sup>2</sup> + im<sub>i</sub><sup>2</sup>),<BR>phase<sub>i</sub> see ''poffset''</code>
-|L+2
-|-
-|'''2'''
-|amplitude spectrum
-|<code>{ amp<sub>0</sub>, amp<sub>1</sub>, ... }</code>
-|L+1
-|-
-|'''3'''
-|power spectrum
-|<code>{ amp<sub>0</sub><sup>2</sup>, amp<sub>1</sub><sup>2</sup>, ... }</code>
-| L+1
-|-
-|'''4'''
-|logarithmic amplitude spectrum
-|<code>{ lev<sub>0</sub>, lev<sub>1</sub>, ... }<BR>with: lev<sub>i</sub>=20*log<sub>10</sub>(amp<sub>i</sub>/''aref'')</code>
-| L+1
-|}
 ----
 ;See also: [[Programmer_Guide/Command_Reference/EVAL/ifft|ifft]], [[Programmer_Guide/Command_Reference/EVAL/dft|dft]], [[Programmer_Guide/Command_Reference/EVAL/dct|dct]], [[Programmer_Guide/Command_Reference/EVAL/cepstrum|cepstrum]], [[Programmer_Guide/Command_Reference/EVAL/lpc|lpc]], [[Programmer_Guide/Command_Reference/EVAL/complex arithmetic|complex arithmetic]]
 [[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
-{{DISPLAYTITLE:{{SUBPAGENAME}}}}
-=====cepstrum=====
-Cepstrum.
-=====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.

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

Revision as of 13:35, 12 April 2011

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