rfft
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## rfft

rfft — Fast Fourier Transform of a real-value array.

## Description

Applies a forward Fast Fourier Transform to a real-value input 1-dimensional array. The output is another array containing the transform, non-redundant, non-negative spectrum only. If the input array is power-of-two, the output array size will match the input size, with the first two points containing 0Hz and Nyquist frequency coefficients. Otherwise, the output will have two extra values (input size + 2), and the the Nyquist coefficient will be placed at kin[input_size] position (kin[1] and kin[input_size+1] will be 0].

## Syntax

    kout[] rfft kin[]

## Performance

kout[] -- output array containing the transform. It will be created if it does not exist.

kin[] -- input array containing the real-valued input.

## Examples

Here is an example of the rfft opcode. It uses the file rfft.csd.

Example 896. Example of the rfft opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

    <CsoundSynthesizer>

    <CsOptions>
    -d -o dac
    </CsOptions>

    <CsInstruments>
    ;ksmps needs to be an integer div of hopsize
    ksmps = 64
    0dbfs=1

    instr 1

     ihopsize = 256   ; hopsize
     ifftsize = 1024  ; FFT size
     iolaps = ifftsize/ihopsize ; overlaps
     ibw = sr/ifftsize ; bin bandwidth
     kcnt init 0    ; counting vars
     krow init 0

     kOla[] init ifftsize ; overlap-add buffer
     kIn[] init ifftsize  ; input buffer
     kSw[] init ifftsize
     kOut[][] init iolaps, ifftsize ; output buffers

     a1 diskin2 "fox.wav",1,0,1 ; audio input
     ks  expon  100, p3, 1000
     asw vco2  0.15, ks

     /* every hopsize samples */
     if kcnt == ihopsize then
       /* window and take FFT */
       kWin[] window kIn,krow*ihopsize
       kSpec[] rfft kWin
       kWin window kSw,krow*ihopsize
       kSpec2[] rfft kWin
       kProd[] cmplxprod kSpec, kSpec2

       /* IFFT + window */
       kRow[] rifft kProd + kSpec
       kWin window kRow, krow*ihopsize
       /* place it on out buffer */
       kOut setrow kWin, krow

       /* zero the ola buffer */
       kOla = 0
       /* overlap-add */
       ki = 0
       until ki == iolaps do
         kRow getrow kOut, ki
         kOla = kOla + kRow
         ki += 1
       od

      /* update counters */
      krow = (krow+1)%iolaps
      kcnt = 0
     endif

     /* shift audio in/out of buffers */
     kIn shiftin a1
     kSw shiftin asw
     a2 shiftout kOla
        out a2/iolaps

     /* increment counter */
     kcnt += ksmps

    endin

    </CsInstruments>

    <CsScore>
    i1 0 10
    </CsScore>

    </CsoundSynthesizer>

## See Also

Vectorial opcodes, array opcodes

## Credits

Author: Victor Lazzarini
NUI Maynooth
2014

New in version 6.04

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