Programmer Guide/Command Reference/EVAL/dft: Difference between revisions

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:;<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:
;Result:A vector ''y'' containing the result of the transformation. The length and content of ''y'' depends on ''x'' and ''type''.
:{|class="einrahmen"
!''type'' !! ''x'' !! nrow(''x'') !! ''y'' !! nrow(''y'') !! description
|-
|0
|real signal with N samples
|N
|complex spectrum with N/2+1 values
|N+2
|real->complex forward dft<BR>note: only the first half of the conj. sym. complex spectrum is stored in ''y''
|-
|}
;See also: [[Programmer_Guide/Command_Reference/EVAL/fft|fft]], [[Programmer_Guide/Command_Reference/EVAL/ifft|ifft]], [[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]]


<code>dft(<var>xr</var>)</code>
[[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
 
=====Function:=====
 
Forward DFT of the real signal <var>xr</var>. <code>nrow(xr)</code> must be even.
 
=====Result:=====
 
A complex spectrum with <code>nrow(xr)/2</code> complex elements (1st half).
 
=====Usage:=====
 
<code>dft(<var>xc</var>, 1)</code>
 
=====Function:=====
 
Forward DFT of the complex signal <var>xc</var>.
 
=====Result:=====
 
A complex spectrum of the same type as <var>xc</var>.
 
=====Usage:=====
 
<code>dft(<var>xc</var>, 2)</code>
 
=====Function:=====
 
Inverse DFT of the symmetrical complex spectrum.
 
=====Result:=====
 
A real signal with <code>nrow(xc)*2</code> elements.
 
=====Usage:=====
 
<code>dft(<var>xc</var>, 3)</code>
 
=====Function:=====
 
Inverse DFT of the complex spectrum <var>xc</var>.
 
=====Result:=====
 
A complex spectrum of the same type as <var>xc</var>.

Revision as of 11:53, 12 April 2011

Inverse or forward discrete fourier transform (dft).

Usage
dft(x {, type)
xthe 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 real->complex forward dft
note: only the first half of the conj. sym. complex spectrum is stored in y
See also
fft, ifft, dct, cepstrum, lpc, , complex arithmetic

<function list>

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