Programmer Guide/Command Reference/EVAL/ifft: Difference between revisions
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{{DISPLAYTITLE:{{SUBPAGENAME}}}} | {{DISPLAYTITLE:{{SUBPAGENAME}}}} | ||
===== | Compute the discrete fourier transform of a real signal using the '''fft''' or the '''dft''' algorithm. | ||
---- | |||
{| | ;Usage 1:<code>fft(<var>n</var>)</code> | ||
:;<var>n</var>: desired signal window length (scalar) | |||
;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]) - 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}}}} | |||
// ifft( Y , YFORMAT=0 , POFFSET=0 , PRANGE=0 ) | |||
// function: | |||
// Y vector or matrix, each row contains a complex spectrum | |||
// YFORMAT input format | |||
// YFORMAT=0 -> complex (re0 im0 re1 im1 ..) | |||
// YFORMAT=1 -> complex polar (amp0 phase0 amp1 phase1 ..) | |||
// POFFSET phase locking offset (sample offset to the signal begin or to the selected "zero phase position") | |||
// PRANGE phase range | |||
// PRANGE=0 -> phase values are in the range 0..2*pi | |||
// PRANGE=1 -> phase values are in the range -pi..pi | |||
// result: | |||
// vector or matrix X containing one real timesignal | |||
// ncol(X) = ncol(Y) | |||
// nrow(X) = nrow(Y)-2 | |||
Revision as of 12:09, 12 April 2011
Compute the discrete fourier transform of a real signal using the fft or the dft algorithm.
- Usage 1
fft(n)- n
- desired signal window length (scalar)
- Result 1
- The next (nearest) possible signal window length.
- Usage 2
fft(x)- x
- signal vector or matrix; if x is a matrix a spectrum of each column is computed
- Result 2
- A matrix y with 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(nrow(x)).
- Usage 3
fft(x, n {, ytype, poffset, prange, aref})- x
- signal vector or matrix; if x is a matrix a spectrum of each column is computed
- n
- desired length of analysis window;
- If
n < nrow(x), 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(x), zero padding is applied to the signal.
- If
- ytype
- select the type and format of the computed spectrum (default=0) -> see Result 3
- poffset
- offset in samples to the signal begin or the selected zero phase position (default=0)
poffset=0 -> phase[i] = atan2(im[i], re[i])otherwise -> phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * poffset) % (2 * pi)
- prange
- selects the range of phase values (default=0)
prange='0 -> 0 <= phase[i] < 2*piotherwise -> -pi <= phase[i] < pi
- aref
- reference amplitude if the log. spectrum (ytype=4) is requested (default=1)
- Result 3
- A matrix y with 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.
ytype description content of y[*,j] nrow(y) 0 complex spectrum in cartesian format { re0, im0, re1, im1, ... }L+2 1 complex spectrum in polar format { amp0, phase0, amp1, phase1, ... }
with: ampi=sqrt(rei2 + imi2),
phasei see poffsetL+2 2 amplitude spectrum { amp0, amp1, ... }L+1 3 power spectrum { amp02, amp12, ... }L+1 4 logarithmic amplitude spectrum { lev0, lev1, ... }
with: levi=20*log10(ampi/aref)L+1
// ifft( Y , YFORMAT=0 , POFFSET=0 , PRANGE=0 ) // function: // Y vector or matrix, each row contains a complex spectrum // YFORMAT input format // YFORMAT=0 -> complex (re0 im0 re1 im1 ..) // YFORMAT=1 -> complex polar (amp0 phase0 amp1 phase1 ..) // POFFSET phase locking offset (sample offset to the signal begin or to the selected "zero phase position") // PRANGE phase range // PRANGE=0 -> phase values are in the range 0..2*pi // PRANGE=1 -> phase values are in the range -pi..pi // result: // vector or matrix X containing one real timesignal // ncol(X) = ncol(Y) // nrow(X) = nrow(Y)-2
