Programmer Guide/Command Reference/EVAL/dft: Difference between revisions
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Inverse or forward discrete fourier transform (dft). | Inverse or forward discrete fourier transform (dft). | ||
;Usage:<code>dft(<var>x</var> {, <var>type</var>)</code> | ;Usage:<code>dft(<var>x</var> {, <var>type</var>)</code> | ||
:;<var>x</var>the data vector to be transformed | :;<var>x</var>:the data vector to be transformed | ||
:;<var>type</var>:selects the data type of the argument and result and the transformation to be performed (default=0) | :;<var>type</var>:selects the data type of the argument and result and the transformation to be performed (default=0) | ||
;Result:A vector ''y'' containing the result of the transformation. The length and content of ''y'' depends on ''x'' and ''type''. | ;Result:A vector ''y'' containing the result of the transformation. The length and content of ''y'' depends on ''x'' and ''type''. | ||
| Line 8: | Line 8: | ||
!''type'' !! ''x'' !! nrow(''x'') !! ''y'' !! nrow(''y'') !! description | !''type'' !! ''x'' !! nrow(''x'') !! ''y'' !! nrow(''y'') !! description | ||
|- | |- | ||
|0 | |'''0''' | ||
|real signal with N samples | |real signal with N samples | ||
|N | |N | ||
|complex spectrum with N/2+1 values | |complex spectrum with N/2+1 values | ||
|N+2 | |N+2 | ||
|real | |forward <code>real→complex</code> dft<BR>note: only the first half (values: 0..N/2) of the conj. sym. complex spectrum is stored in ''y'' | ||
|- | |||
|'''1''' | |||
|complex signal with N samples | |||
|2N | |||
|complex spectrum with N values | |||
|2N | |||
|forward <code>complex→complex</code> dft | |||
|- | |||
|'''2''' | |||
|first half (values: 0..N/2) of a conj. sym. complex spectrum | |||
|N+2 | |||
|real signal with N samples | |||
|N | |||
|inverse <code>complex→real</code> dft<BR>note: this is the inverse of ''type''=0 | |||
|- | |||
|'''3''' | |||
|complex spectrum with N values | |||
|2N | |||
|complex signal with N samples | |||
|2N | |||
|inverse <code>complex→complex</code> dft | |||
|- | |- | ||
|} | |} | ||
;See also: [[ | ;See also: [[../fft|fft]], [[../ifft|ifft]], [[../dct|dct]], [[../cepstrum|cepstrum]], [[../lpc|lpc]], [[../complex arithmetic|complex arithmetic]] | ||
[[ | [[../#Functions|<function list>]] | ||
Latest revision as of 09:14, 18 April 2018
Inverse or forward discrete fourier transform (dft).
- Usage
dft(x {, type)- x
- the data vector to be transformed
- type
- selects the data type of the argument and result and the transformation to be performed (default=0)
- Result
- A vector y containing the result of the transformation. The length and content of y depends on x and type.
type x nrow(x) y nrow(y) description 0 real signal with N samples N complex spectrum with N/2+1 values N+2 forward real→complexdft
note: only the first half (values: 0..N/2) of the conj. sym. complex spectrum is stored in y1 complex signal with N samples 2N complex spectrum with N values 2N forward complex→complexdft2 first half (values: 0..N/2) of a conj. sym. complex spectrum N+2 real signal with N samples N inverse complex→realdft
note: this is the inverse of type=03 complex spectrum with N values 2N complex signal with N samples 2N inverse complex→complexdft
