FFT Overview:

Filter: SuperCollider implements a number of UGens supporting Fast Fourier Transform (FFT) based processing. The most basic of these are FFT and IFFT (inverse-FFT) which convert data between the time and frequency domains:

FFT requires a Buffer or LocalBuf. The buffer's size must correspond to a power of 2, and must also be a multiple of the server's current block size. The window size is equivalent to the buffer size, and the window overlap defaults to 2 (hop = 0.5). Both FFT and IFFT use a sine window by default. Their combination efficiently becomes a Hanning window (i.e. raised sine, that is, sine squared).

FFT stores spectral data in the buffer, in the following format:

DC | nyquist | real 1f | imag 1f | real 2f | imag 2f | ... | real (N-1)f | imag (N-1)f |

where `f`

is the frequency corresponding to the window size, and `N`

is the window size / 2.

The `FFT`

UGen returns a signal (usually called **chain**) is constant at `-1`

, only when a new FFT window starts, the signal equals the buffer number. This is how subsequent FFT UGens can write to that buffer and know when to do this. The FFT information is not in the chain signal, but in the buffer.

In between an FFT and an IFFT one can chain together a number of Phase Vocoder UGens (i.e. `PV_...`

) to manipulate blocks of spectral data before reconversion. The process of buffering the appropriate amount of audio, windowing, conversion, overlap-add, etc. is handled automatically.

See PV and FFT UGens in the Standard Library for a list of UGens.

In order to expand PV UGens for a multichannel input signal, an appropriate array of buffers must be provided (not a multichannel buffer):

For more examples, see Multichannel Expansion with FFT UGens

PV Ugens write their output data *in place*, i.e. back into the same buffer from which they read. PV UGens which require two buffers write their data into the first buffer, usually called 'bufferA'.

A similar example using a soundfile:

Because each PV UGen overwrites the output of the previous one, it is necessary to copy the data to an additional buffer at the desired point in the chain in order to do parallel processing of input without using multiple FFT UGens. PV_Copy allows for this.

NOTE: As of SC 3.7 instances of PV_Copy are added automatically where necessary for parallel processing. Existing code explicitly using PV_Copy should continue to work.

PV processes can also share a single FFT ugen to process a signal in parallel. In the following example, 'chain0' and 'chain1' share the same FFT ugen. SuperCollider automatically copies the FFT data from 'chain' into hidden LocalBufs inside the Synth. In the following example, if the PV_PhaseShift UGen were operating directly on `chainA`

, then the two IFFT units would produce the same signal, which, when added together, would reinforce each other. Instead, the sound is nearly silent -- proving that `chainB`

is in a different buffer, even though the function does not explicitly create it.

Note that PV UGens convert as needed between cartesian (complex) and polar representations, therefore when using multiple PV UGens it may be impossible to know in which form the values will be at any given time. FFT produces complex output (see above). The following, however, returns a reliable magnitude plot:

It is possible to manipulate the FFT data directly within a synth graph (if there doesn't already exist a PV UGen which will do what you want), using the methods pvcalc, pvcalc2, pvcollect. Here's an example which uses the methods SequenceableCollection: -clump and SequenceableCollection: -flop to rearrange the order of the spectral bins:

Care must be taken when using multichannel expansion with FFT UGens, as they require separate buffers. Code such as this can be deceptive:

The above may seem to work, but does not. It does result in two FFT UGens, but as they both write to the same buffer, the second simply overwrites the data from the first, thus wasting CPU and accomplishing nothing.

When using multichannel expansion with FFT UGens it is necessary to ensure that each one writes to a different buffer. Here's an example of one way to do this:

Note that dup on a UGen just makes a reference to that UGen, because UGen defines -copy to simply return the receiver. (See UGen for more detail.)

Code like `IFFT(chain).dup`

is found throughout the PV help files , and is just a convenient way to copy a mono signal to stereo, without further computation.

See also Multichannel Expansion.

The following PV UGens are included in the standard SC distribution:

- FFT
- Fast Fourier Transform
- IFFT
- Inverse Fast Fourier Transform
- PV_Add
- complex addition
- PV_BinScramble
- scramble bins
- PV_BinShift
- shift and stretch bin position
- PV_BinWipe
- combine low and high bins from two inputs
- PV_BrickWall
- zero bins
- PV_ConformalMap
- complex plane attack
- PV_CopyPhase
- copy magnitudes and phases
- PV_Diffuser
- random phase shifting
- PV_HainsworthFoote
- onset detection
- PV_JensenAndersen
- onset detection
- PV_LocalMax
- pass bins which are a local maximum
- PV_MagAbove
- pass bins above a threshold
- PV_MagBelow
- pass bins below a threshold
- PV_MagClip
- clip bins to a threshold
- PV_MagFreeze
- freeze magnitudes
- PV_MagMul
- multiply magnitudes
- PV_MagDiv
- division of magnitudes
- PV_MagNoise
- multiply magnitudes by noise
- PV_MagShift
- shift and stretch magnitude bin position
- PV_MagSmear
- average magnitudes across bins
- PV_MagSquared
- square magnitudes
- PV_Max
- maximum magnitude
- PV_Min
- minimum magnitude
- PV_Mul
- complex multiply
- PV_PhaseShift
- shift phase of all bins
- PV_PhaseShift270
- shift phase by 270 degrees
- PV_PhaseShift90
- shift phase by 90 degrees
- PV_RandComb
- pass random bins
- PV_RandWipe
- crossfade in random bin order
- PV_RectComb
- make gaps in spectrum
- PV_RectComb2
- make gaps in spectrum
- UnpackFFT, PackFFT, Unpack1FFT
- "unpacking" components used in pvcalc, pvcalc2, pvcollect (can also be used on their own)

For a full list of FFT UGens, see **UGens>FFT** in the Browse: UGens>FFT page.

helpfile source: /usr/local/share/SuperCollider/HelpSource/Guides/FFT-Overview.schelp

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