Programmer Guide/Command Reference/EVAL/cepstrum - Revision history

Christian at 18:26, 21 April 2011

2011-04-21T18:26:17Z

193.171.195.48 at 09:20, 21 April 2011

2011-04-21T09:20:34Z

← Older revision		Revision as of 11:20, 21 April 2011
Line 26:		Line 26:
	;Result 2:A vector with same length as ''x'', containing the liftered spectrum.		;Result 2:A vector with same length as ''x'', containing the liftered spectrum.
	----		----
	;See also: [[~~Programmer_Guide/Command_Reference/EVAL~~/fft\|fft]], [[~~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~~/lpc\|lpc]], [[~~Programmer_Guide~~/~~Command_Reference/EVAL~~/~~complex arithmetic~~\|~~complex arithmetic~~]]		;See also: [[../fft\|fft]], [[../ifft\|ifft]], [[../dft\|dft]], [[../dct\|dct]], [[../lpc\|lpc]], [[../ipeak\|ipeak]], [[../formants\|formants]]

	[[~~Programmer_Guide~~/~~Command_Reference/EVAL~~#Functions\|<function list>]]		[[../#Functions\|<function list>]]

Toni at 12:36, 12 April 2011

2011-04-12T12:36:43Z

← Older revision		Revision as of 14:36, 12 April 2011
Line 26:		Line 26:
	;Result 2:A vector with same length as ''x'', containing the liftered spectrum.		;Result 2:A vector with same length as ''x'', containing the liftered spectrum.
	----		----
	;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]]		;See also: [[Programmer_Guide/Command_Reference/EVAL/fft\|fft]], [[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/lpc\|lpc]], [[Programmer_Guide/Command_Reference/EVAL/complex arithmetic\|complex arithmetic]]

	[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]		[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]

Toni at 12:35, 12 April 2011

2011-04-12T12:35:44Z

← Older revision		Revision as of 14:35, 12 April 2011
Line 4:		Line 4:
	;Usage 1:<code>cepstrum(<var>x</var>)</code>		;Usage 1:<code>cepstrum(<var>x</var>)</code>
	:;<var>x</var>: a vector containing a log. amplitude spectrum		:;<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</code> samples (<code>-> nrow(''x'')=L/2+1=2^M/2+1</code>).		::*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>-> 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''.		;Result 1:A vector with <code>L/2</code> values, containing the coefficients or the real cepstrum of ''x''.
	----		----

Toni at 12:35, 12 April 2011

2011-04-12T12:35:12Z

Show changes

Toni at 12:20, 12 April 2011

2011-04-12T12:20:43Z

← Older revision		Revision as of 14:20, 12 April 2011
Line 1:		Line 1:
			{{DISPLAYTITLE:{{SUBPAGENAME}}}}
			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 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>).
			;Result 1:The next (nearest) possible signal window length.
			----
			;Usage 2:<code>fft(<var>x</var>)</code>
			:;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed
			;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''))]].
			----
			;Usage 3:<code>fft(<var>x</var>, <var>n</var> {, <var>ytype</var>, <var>poffset</var>, <var>prange</var>, <var>aref</var>})</code>
			:;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed
			:;<var>n</var>: desired length of analysis window;
			::*If <code>''n'' < nrow(''x'')</code>, the analysis window length L is set to nrow(''x''), otherwise L is set to ''n''.
			::*If the analysis window length L is a power of 2 (L=2^M), the '''fft''' algorithm is used, otherwise the '''dft''' is used.
			::*If L is greater than [[../nrow\|nrow(''x'')]], zero padding is applied to the signal.
			:;<var>ytype</var>: select the type and format of the computed spectrum (default=0) -> see '''Result 3'''
			:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0)
			:::{\|class="keinrahmen"
			\|''poffset''='''0''' \|\|-> <code>phase[i] = atan2(im[i], re[i])</code>
			\|-
			\|otherwise \|\|-> <code>phase[i] = (atan2(im[i], re[i]) - 2pii/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}}}}		{{DISPLAYTITLE:{{SUBPAGENAME}}}}
	=====cepstrum=====		=====cepstrum=====

Admin: 1 revision: Initial import

2010-11-18T16:31:41Z

1 revision: Initial import

← Older revision	Revision as of 18:31, 18 November 2010
(No difference)

193.171.195.8: initial import

2010-05-17T13:05:27Z

initial import

New page

{{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.

← Older revision		Revision as of 20:26, 21 April 2011
Line 4:		Line 4:
	;Usage 1:<code>cepstrum(<var>x</var>)</code>		;Usage 1:<code>cepstrum(<var>x</var>)</code>
	:;<var>x</var>: a vector containing a log. amplitude spectrum		:;<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>-> nrow(''x'')=L/2+1=2^M/2+1</code>).		::*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>→ 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''.		;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>		;Usage 2:<code>cepstrum(<var>x</var>, <var>m</var>)</code>
	:;<var>x</var>: a vector containing a log. amplitude spectrum		:;<var>x</var>: a vector containing a log. amplitude spectrum
	:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' <= L/2		:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' ≤ L/2
	;Description:		;Description:
	:# The real cepstrum ''c'' of ''x'' is computed.		:# The real cepstrum ''c'' of ''x'' is computed.
Line 19:		Line 19:
	:;<var>x</var>: a vector containing a log. amplitude spectrum		:;<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>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'' <= L/2-''o''		:;<var>m</var>: the number of coefficients to be used for smoothing; 0 < ''m'' ≤ L/2-''o''
	;Description:		;Description:
	:# The real cepstrum ''c'' of ''x'' is computed.		:# The real cepstrum ''c'' of ''x'' is computed.