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

193.171.195.48 at 09:56, 21 April 2011

2011-04-21T09:56:46Z

← Older revision		Revision as of 11:56, 21 April 2011
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	\|}		\|}
	:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).		:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).
	;Result 3: A matrix ''y'' with [[../ncol\|ncol(''x'')]] columns, where each column ''y''[,j] contains the result of the inverse transform (the real valued signal) of the column ''x''[,j]. Each signal vector ''y''[*,j] consists of <code>L</code> (real) samples.		;Result: A matrix ''y'' with [[../ncol\|ncol(''x'')]] columns, where each column ''y''[,j] contains the result of the inverse transform (the real valued signal) of the column ''x''[,j]. Each signal vector ''y''[*,j] consists of <code>L</code> (real) samples.
	;See also: [[../fft\|fft]], [[../dft\|dft]], [[../dct\|dct]], [[../cepstrum\|cepstrum]], [[../lpc\|lpc]], [[../complex arithmetic\|complex arithmetic]]		;See also: [[../fft\|fft]], [[../dft\|dft]], [[../dct\|dct]], [[../cepstrum\|cepstrum]], [[../lpc\|lpc]], [[../complex arithmetic\|complex arithmetic]]

	[[../#Functions\|<function list>]]		[[../#Functions\|<function list>]]

193.171.195.48 at 09:56, 21 April 2011

2011-04-21T09:56:09Z

← Older revision		Revision as of 11:56, 21 April 2011
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	:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).		:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).
	;Result 3: A matrix ''y'' with [[../ncol\|ncol(''x'')]] columns, where each column ''y''[,j] contains the result of the inverse transform (the real valued signal) of the column ''x''[,j]. Each signal vector ''y''[*,j] consists of <code>L</code> (real) samples.		;Result 3: A matrix ''y'' with [[../ncol\|ncol(''x'')]] columns, where each column ''y''[,j] contains the result of the inverse transform (the real valued signal) of the column ''x''[,j]. Each signal vector ''y''[*,j] consists of <code>L</code> (real) samples.
	;See also: [[~~Programmer_Guide/Command_Reference/EVAL~~/fft\|fft]], [[~~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: [[../fft\|fft]], [[../dft\|dft]], [[../dct\|dct]], [[../cepstrum\|cepstrum]], [[../lpc\|lpc]], [[../complex arithmetic\|complex arithmetic]]

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

Christian at 14:12, 13 April 2011

2011-04-13T14:12:50Z

← Older revision		Revision as of 16:12, 13 April 2011
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	:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)		:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"
	\|''prange''='''0''' \|\|→ <code>0 <= phase[i] < 2*pi</code>		\|''prange''='''0''' \|\|→ <code>0 ≤ phase[i] < 2*pi</code>
	\|-		\|-
	\|otherwise \|\|→ <code>-pi <= phase[i] < pi</code>		\|otherwise \|\|→ <code>-pi ≤ phase[i] < pi</code>
	\|}		\|}
	:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).		:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).

Christian at 13:49, 13 April 2011

2011-04-13T13:49:06Z

← Older revision		Revision as of 15:49, 13 April 2011
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	;Usage:<code>ifft(<var>x</var>, {, <var>xtype</var>, <var>poffset</var>, <var>prange</var>})</code>		;Usage:<code>ifft(<var>x</var>, {, <var>xtype</var>, <var>poffset</var>, <var>prange</var>})</code>
	:;<var>x</var>: complex spectrum vector or matrix; if ''x'' is a matrix an inverse transform is computed for each column		:;<var>x</var>: complex spectrum vector or matrix; if ''x'' is a matrix an inverse transform is computed for each column
	::*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex->real</code> version of the inverse transformation is used and the results are real numbered signals.		::*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex→real</code> version of the inverse transformation is used and the results are real numbered signals.
	::Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2(N-1)</code>		::Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2(N-1)</code>
	::*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M</code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.		::*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M</code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.
	:;<var>xtype</var>: select the complex number format of ''x'' (default=0)		:;<var>xtype</var>: select the complex number format of ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"
	\|''xtype''='''0''' \|\|-> cartesian <code>{ re, im, .. }</code>		\|''xtype''='''0''' \|\|→ cartesian <code>{ re, im, .. }</code>
	\|-		\|-
	\|otherwise \|\|-> polar <code>{ amp, phase, .. }</code>		\|otherwise \|\|→ polar <code>{ amp, phase, .. }</code>
	\|}		\|}
	:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0); If this value is not equal 0, the phase values stored in ''x'' are '''locked''' (see [[../fft\|fft]]) and must be transformed to '''normal''' phase values before the inverse ft-transform is performed.		:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0); If this value is not equal 0, the phase values stored in ''x'' are '''locked''' (see [[../fft\|fft]]) and must be transformed to '''normal''' phase values before the inverse ft-transform is performed.
	:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)		:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"
	\|''prange''='''0''' \|\|-> <code>0 <= phase[i] < 2*pi</code>		\|''prange''='''0''' \|\|→ <code>0 <= phase[i] < 2*pi</code>
	\|-		\|-
	\|otherwise \|\|-> <code>-pi <= phase[i] < pi</code>		\|otherwise \|\|→ <code>-pi <= phase[i] < pi</code>
	\|}		\|}
	:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).		:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).

Toni at 11:30, 12 April 2011

2011-04-12T11:30:02Z

← Older revision		Revision as of 13:30, 12 April 2011
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	:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)		:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"
	\|''prange''='''0'' \|\|-> <code>0 <= phase[i] < 2*pi</code>		\|''prange''='''0''' \|\|-> <code>0 <= phase[i] < 2*pi</code>
	\|-		\|-
	\|otherwise \|\|-> <code>-pi <= phase[i] < pi</code>		\|otherwise \|\|-> <code>-pi <= phase[i] < pi</code>

Toni at 11:29, 12 April 2011

2011-04-12T11:29:38Z

← Older revision		Revision as of 13:29, 12 April 2011
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	\|otherwise \|\|-> polar <code>{ amp, phase, .. }</code>		\|otherwise \|\|-> polar <code>{ amp, phase, .. }</code>
	\|}		\|}
	:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0)		:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0); If this value is not equal 0, the phase values stored in ''x'' are '''locked''' (see [[../fft\|fft]]) and must be transformed to '''normal''' phase values before the inverse ft-transform is performed.
	:If this value is not equal 0, the phase values stored in ''x'' are '''locked''' (see [[../fft\|fft]]) and must be transformed to '''normal''' phase values before the inverse ft-transform is performed.
	:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)		:;<var>prange</var>: selects the range of phase values stored in ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"

Toni at 11:29, 12 April 2011

2011-04-12T11:29:16Z

← Older revision		Revision as of 13:29, 12 April 2011
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	::*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex->real</code> version of the inverse transformation is used and the results are real numbered signals.		::*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex->real</code> version of the inverse transformation is used and the results are real numbered signals.
	::Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2(N-1)</code>		::Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2(N-1)</code>
	::*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M<code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.		::*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M</code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.
	:;<var>xtype</var>: select the complex number format of ''x'' (default=0)		:;<var>xtype</var>: select the complex number format of ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"

Toni at 11:28, 12 April 2011

2011-04-12T11:28:40Z

← Older revision		Revision as of 13:28, 12 April 2011
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	;Usage:<code>ifft(<var>x</var>, {, <var>xtype</var>, <var>poffset</var>, <var>prange</var>})</code>		;Usage:<code>ifft(<var>x</var>, {, <var>xtype</var>, <var>poffset</var>, <var>prange</var>})</code>
	:;<var>x</var>: complex spectrum vector or matrix; if ''x'' is a matrix an inverse transform is computed for each column		:;<var>x</var>: complex spectrum vector or matrix; if ''x'' is a matrix an inverse transform is computed for each column
	:*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex->real</code> version of the inverse transformation is used and the results are real numbered signals.		::*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex->real</code> version of the inverse transformation is used and the results are real numbered signals.
	:Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2(N-1)</code>		::Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2(N-1)</code>
	:*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M<code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.		::*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M<code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.
	:;<var>xtype</var>: select the complex number format of ''x'' (default=0)		:;<var>xtype</var>: select the complex number format of ''x'' (default=0)
	:::{\|class="keinrahmen"		:::{\|class="keinrahmen"

Toni at 11:28, 12 April 2011

2011-04-12T11:28:16Z

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:{{SUBPAGENAME}}}}
-Compute the discrete fourier transform of a real signal using the '''fft''' or the '''dft''' algorithm.
+Compute the inverse discrete fourier transform of a (conj. sym.) complex spectrum using the inverse '''fft''' or '''dft''' algorithm.
 ----
-;Usage 1:<code>fft(<var>n</var>)</code>
+;Usage:<code>ifft(<var>x</var>, {, <var>xtype</var>, <var>poffset</var>, <var>prange</var>})</code>
-:;<var>n</var>: desired signal window length (scalar)
+:;<var>x</var>: complex spectrum vector or matrix; if ''x'' is a matrix an inverse transform is computed for each column
-;Result 1:The next (nearest) possible signal window length.
+:*The spectra stored in ''x'' must be the 1st half of conj. sym. spectra, because a <code>complex->real</code> version of the inverse transformation is used and the results are real numbered signals.
-----
+:*Each spectrum consists of <code>N=nrow(''x'')/2</code> complex values. The transformation length is set to <code>L=2*(N-1)</code>
-;Usage 2:<code>fft(<var>x</var>)</code>
+:*If the transformation length <code>L</code> is a power of 2 (<code>L=2^M<code>), the inverse '''fft''' algorithm is used, otherwise the inverse '''dft''' is used.
-:;<var>x</var>: signal vector or matrix; if ''x'' is a matrix a spectrum of each column is computed
+:;<var>xtype</var>: select the complex number format of ''x'' (default=0)
 :::{|class="keinrahmen"
-|''poffset''='''0''' ||-> <code>phase[i] = atan2(im[i], re[i])</code>
+|''xtype''='''0''' ||-> cartesian <code>{ re, im, .. }</code>
 |-
-|otherwise ||-> <code>phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * ''poffset'') % (2 * pi)</code>
+|otherwise ||-> polar <code>{ amp, phase, .. }</code>
 |}
-:;<var>prange</var>: selects the range of phase values (default=0)
+:;<var>poffset</var>: offset in samples to the signal begin or the selected ''zero phase'' position (default=0)
 :::{|class="keinrahmen"
 |''prange''='''0'' ||-> <code>0 <= phase[i] < 2*pi</code>
@@ Line 29: / Line 21: @@
 |otherwise ||-> <code>-pi <= phase[i] < pi</code>
 |}
-:;<var>aref</var>: reference amplitude if the log. spectrum (''ytype''=4) is requested (default=1)
+:*The arguments ''poffset'' and ''prange'' are ignored if ''xtype'' equals '''0''' (''x'' in cartesian format).
-;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''.
+;Result 3: A matrix ''y'' with [[../ncol|ncol(''x'')]] columns, where each column ''y''[*,j] contains the result of the inverse transform (the real valued signal) of the column ''x''[*,j]. Each signal vector ''y''[*,j] consists of <code>L</code> (real) samples.
-::{|class="einrahmen"
+;See also: [[Programmer_Guide/Command_Reference/EVAL/fft|fft]], [[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>]]

193.171.195.48 at 11:09, 12 April 2011

2011-04-12T11:09:03Z

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:{{SUBPAGENAME}}}}
-=====ifft=====
+Compute the discrete fourier transform of a real signal using the '''fft''' or the '''dft''' algorithm.
+----
-{|
+;Usage 1:<code>fft(<var>n</var>)</code>
 |-
-|ifft(x)
+|'''4'''
-|The inverse FFT of the vector x. The argument <var>x</var> must be a complex vector with 2^(m-1)+1 complex values. The result is a real signal with 2^m values.
+|logarithmic amplitude spectrum
 |}