Programmer Guide/Command Reference/EVAL/fft: Difference between revisions
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;Result: 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: 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" | ::{|class="einrahmen" | ||
!''ytype'' !! content of y[*,j] !! nrow(y) | !''ytype'' !! description !! content of y[*,j] !! nrow(y) | ||
|- | |- | ||
|'''0''' | |'''0''' | ||
|the 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''' | |'''1''' | ||
|the complex spectrum in polar format | |||
|<code>{ amp<sub>0</sub>, phase<sub>0</sub>, amp<sub>1</sub>, phase<sub>1</sub>, ... }</code> | |||
|L+2 | |||
|- | |- | ||
|'''2''' | |'''2''' | ||
{ amp<sub>0</sub>, amp<sub>1</sub>, ... }</ | |the amplitude spectrum | ||
|<code>{ amp<sub>0</sub>, amp<sub>1</sub>, ... }</code> | |||
|L+1 | |||
|- | |||
|'''3''' | |||
|the power spectrum | |||
|<code>{ amp<sub>0</sub><sup>2</sub>, amp<sub>1</sub><sub>2</sub>, ... }</code> | |||
| L+1 | | L+1 | ||
|- | |- | ||
|''' | |'''4''' | ||
|the logarithmic amplitude spectrum | |||
<code>{ lev<sub>0</sub>, lev<sub>1</sub>, ... }<BR>with: lev<sub>i</sub>=20*log<sub>10</sub>(lev<sub>i</sub>/''aref'')</code> | |||
| L+1 | |||
|} | |} | ||
Revision as of 11:27, 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 (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
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
- 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 the complex spectrum in cartesian format { re0, im0, re1, im1, ... }L+2 1 the complex spectrum in polar format { amp0, phase0, amp1, phase1, ... }L+2 2 the amplitude spectrum { amp0, amp1, ... }L+1 3 the power spectrum { amp02, amp12, ... }L+1 4 the logarithmic amplitude spectrum { lev0, lev1, ... }
with: levi=20*log10(levi/aref)L+1
