The Pd Spectral Toolkit facilitates spectral processing in Pd by providing objects that perform frequently used data transformations and calculations. This reduces the number of lower-level objects required to build patches while affording novel data interfaces and utilities, allowing users to spend less time making abstractions and more time implementing complex data manipulation algorithms. Currently the toolkit is compiled only for OS X.

Credits
The Pd Spectral Toolkit was created by Cooper Baker under the supervision of Tom Erbe, supported by a grant from the University of California San Diego between 2012 and 2013. Special thanks to Miller Puckette for invaluable insight regarding spectral math and the Pd api.

This work was published in the 2013 proceedings of the International Computer Music Conference:

Baker, C., Erbe, T. "Pd Spectral Toolkit", Proceedings of the International Computer Music Conference, Pp. 410-413, Perth, Australia, 2013.

Installation
· Copy "Pd Spectral Toolkit" folder to "/Library/Pd/Pd Spectral Toolkit", creating /Library/Pd if it does not exist.
· Add "/Library/Pd/Pd Spectral Toolkit" to Pd's search paths (under Pd menu: Preferences -> Path...)
· Click Apply then Ok
· Restart Pd

Download
Pd Spectral Toolkit.zip
Pd Spectral Toolkit Article.zip
Pd Spectral Toolkit Xcode Project.zip
Pd Spectral Toolkit Source Code.zip
Pd Spectral Toolkit Poster.zip

Code Browser
Source Code

Object Categories
comparison
!&&~ !=~ !||~ &&~ <=~ <~ ==~ >=~ >~ ||~
operator
!~ %~ cmplxabs~ cmplxadd~ cmplxdiv~ cmplxmult~ cmplxsqrt~ cmplxsub~ recip~ rounder~ trunc~
conversion
amptodb~ amptomag~ cartoamp~ cartodb~ cartofreq~ cartomag~ cartophase~ cartopolar~ ctltosig~ dbtoamp~ dbtomag~ degtorad~ degtoturn~ freqtocar~ freqtophase~ freqtopolar~ magtoamp~ magtodb~ phasetofreq~ polartocar~ polartofreq~ radtodeg~ radtoturn~ sigtoctl~ turntodeg~ turntorad~
spectral
binindex~ binmax~ binmin~ binmix~ binmonitor~ binsort~ bintrim~ blocksmooth~ freqsieve~ fundfreq~ harmprod~ magtrim~ oscbank~ pafft~ paifft~ partconv~ peaks~ phaseaccum~ phasedelta~ piwrap~ rotate~ valleys~ windower winfft~ winifft~
misc
bitsafe~ countwrap dspbang~ monitor~ rgbtable scale~ softclip~ tabindex~ terminal


Object Index
!&&~logical not and
!=~logical not equal
!||~logical not or
!~not
&&~logical and
%~modulo
<=~logical less than or equal
<~logical less than
==~logical equal
>=~logical greater than or equal
>~logical greater than
||~logical or
amptodb~amplitude to dB-FS decibels conversion
amptomag~amplitude to magnitude conversion
binindex~outputs a ramp with values from zero to block size minus one
binmax~reports maximum bin value and associated data per block
binmin~reports minimum bin value and associated data per block
binmix~mixes inlet 2 values for all matching inlet 1 values and zeroes all others
binmonitor~outputs a float representing the value of a single bin
binsort~sorts spectral data in ascending or descending order
bintrim~zeroes bin values outside of a specified range
bitsafe~fixes infinity and not a number values
blocksmooth~replaces a block's zero values with preceeding adjacent non-zero values
cartoamp~cartesian coordinates to amplitude conversion
cartodb~cartesian coordinates to dB-FS decibels conversion
cartofreq~cartesian coordinates to magnitude and frequency pairs conversion
cartomag~cartesian coordinates to magnitude conversion
cartophase~cartesian coordinates to phase conversion
cartopolar~cartesian coordinates to polar coordinates conversion
cmplxabs~complex absolute value
cmplxadd~complex addition
cmplxdiv~complex division
cmplxmult~complex multiplication
cmplxsqrt~complex square root
cmplxsub~complex subtraction
countwrapbang driven wrapping counter
ctltosig~control range to signal range conversion
dbtoamp~dB-FS decibels to amplitude conversion
dbtomag~dB-FS decibels to magnitude conversion
degtorad~degrees to radians conversion
degtoturn~degrees to turns conversion
dspbang~outputs a bang when dsp is turned on
freqsieve~assigns frequencies and magnitudes to proper bins
freqtocar~magnitude and frequency pairs to cartesian coordinates conversion
freqtophase~frequency to phase conversion
freqtopolar~magnitude and frequency pairs to polar coordinates conversion
fundfreq~reports most prominent fundamental frequency per spectral block
harmprod~harmonic product spectrum
magtoamp~magnitude to amplitude conversion
magtodb~magnitude to dB-FS decibels conversion
magtrim~zeroes bin values outside of a specified magnitude range
monitor~samples a signal and outputs a float every 20 milliseconds
oscbank~oscillator bank for spectral resynthesis
pafft~windowed phase aligned real fast fourier transform
paifft~windowed normalized phase aligned real inverse fast fourier transform
partconv~partitioned convolution with cartesian coordinates
peaks~finds peaks in spectral data and zeroes everything else
phaseaccum~running phase sums for each bin per frame
phasedelta~phase deviation per frame for each bin
phasetofreq~phase to frequency conversion
piwrap~wraps a signal between -pi and pi
polartocar~polar coordinates to cartesian coordinates conversion
polartofreq~polar coordinates to magnitude and frequency pairs conversion
radtodeg~radians to degrees conversion
radtoturn~radians to turns conversion
recip~reciprocal calculation
rgbtableoutputs color values based on input float value
rotate~rotates samples in a signal vector
rounder~rounds decimal values to specified precision
scale~scales values from one range to another
sigtoctl~signal range to control range conversion
softclip~soft clipping waveshaper
tabindex~writes table values at index location
terminalcommand line shell interface
trunc~truncates decimal values to specified precision
turntodeg~turns to degrees conversion
turntorad~turns to radians conversion
valleys~finds valleys in spectral data and zeroes everything else
windowerwrites various window functions into arrays
winfft~windowed real fast fourier transform
winifft~windowed normalized real inverse fast fourier transform


[ !&&~ ] Not And
Performs a logical not and comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ !=~ ] Not Equal
Performs a logical not equal comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ !||~ ] Not Or
Performs a logical not or comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ !~ ] Not
Performs a logical not operation on a signal.

inlet: value
outlet: result

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[ &&~ ] And
Performs a logical and comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ %~ ] Modulo
Performs a modulo operation using the values of two signals and outputs the result.

inlet 1: dividend
inlet 2: divisor
outlet: remainder
argument: divisor

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[ <=~ ] Less Than or Equal
Performs a logical less than or equal comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ <~ ] Less Than
Performs a logical less than comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ ==~ ] Equal
Performs a logical equal comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ >=~ ] Greater Than or Equal
Performs a logical greater than or equal comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ >~ ] Greater Than
Performs a logical greater than comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ ||~ ] Or
Performs a logical or comparison of two signals and outputs 1 or 0.

inlet 1: value a
inlet 2: value b
outlet: result
argument: value b

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[ amptodb~ ] Amplitude to Decibels
Converts amplitude values to dB-FS decibel values.

inlet: amplitude
outlet: decibels

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[ amptomag~ ] Amplitude to Magnitude
Converts amplitude values to magnitude values.

inlet 1: amplitude
inlet 2: overlap factor
outlet: magnitude
argument: overlap factor

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[ binindex~ ] Bin Index
Outputs ascending values from zero to block size minus one for each signal block.

outlet: ascending sample indices

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[ binmax~ ] bin maximum
Outputs the maximum sample value in block a, the associated sample value in block b, and the index location of samples a and b for each signal block.

inlet 1: signal block a
inlet 2: signal block b
outlet 1: maximum a value
outlet 2: associated b value
outlet 3: index of a and b values

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[ binmin~ ] Bin Minimum
Outputs the minimum sample value in block a, the associated sample value in block b, and the index location of samples a and b for each signal block.

inlet 1: signal block a
inlet 2: signal block b
outlet 1: minimum a value
outlet 2: associated b value
outlet 3: index of a and b values

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[ binmix~ ] Bin Mixer
Mixes inlet 2 values for all matching inlet 1 values. Mixed values are placed into location of largest inlet 2 value and all others are zeroed. Operates on one signal vector at a time.

inlet 1: a values
inlet 2: b values
outlet 1: mixed a values
outlet 2: mixed b values

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[ binmonitor~ ] Bin Monitor
Outputs a float representing the value of a specific sample index in the signal vector once per block. Useful for looking at values of particular bins in spectral data.

inlet 1: spectral data
inlet 2: bin number
outlet: bin value float
argument: bin number

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[ binsort~ ] Bin Sort
Sorts Spectral data according to left inlet values and outputs the data in ascending or descending order.

inlet 1: dataset a
inlet 2: dataset b
outlet 1: sorted dataset a
outlet 2: dataset b sorted by a
outlet 3: dataset indices sorted by a
messages: "ascending" or "descending"
arguments: "ascending" or "descending"

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[ bintrim~ ] Bin Trim
Zeroes spectral data outside of a specified bin range.

inlet 1: spectral data a
inlet 2: spectral data b
inlet 3: lower bin number
inlet 4: upper bin number
outlet 1: trimmed data a
outlet 2: trimmed data b
arguments: lower bin, upper bin

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[ bitsafe~ ] Bit Safe
Detects infinity or not a number values and replaces them with float or zero values.

inlet: value
outlet: result

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[ blocksmooth~ ] Block Smooth
Replaces zero values within a signal vector with preceding adjacent non-zero values.

inlet: rough signal
outlet: smooth signal

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[ cartoamp~ ] Cartesian to Amplitude
Converts cartesian coordinates to amplitude values.

inlet 1: real value
inlet 2: imaginary value
inlet 3: overlap factor
outlet: amplitude
argument: overlap factor

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[ cartodb~ ] Cartesian to Decibels
Converts cartesian coordinates to dB-FS decibel values.

inlet 1: real value
inlet 2: imaginary value
inlet 3: overlap factor
outlet: decibels
argument: overlap factor

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[ cartofreq~ ] Cartesian to Frequency
Converts cartesian coordinates to magnitude and frequency pairs.

inlet 1: real value
inlet 2: imaginary value
inlet 3: overlap factor
outlet 1: magnitude
outlet 2: frequency
argument: overlap factor

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[ cartomag~ ] Cartesian to magnitude
Converts cartesian coordinates to magnitude values.

inlet 1: real value
inlet 2: imaginary value
outlet: magnitude

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[ cartophase~ ] Cartesian to Phase
Converts cartesian coordinates to phase values.

inlet 1: real value
inlet 2: imaginary value
outlet: phase

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[ cartopolar~ ] Cartesian to Polar
Converts cartesian coordinates to polar coordinates.

inlet 1: real value
inlet 2: imaginary value
outlet 1: magnitude
outlet 2: phase

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[ cmplxabs~ ] Complex Absolute
Calculates the absolute value of a complex number.

inlet 1: real value
inlet 2: imaginary value
outlet: absolute value

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[ cmplxadd~ ] Complex Addition
Adds two complex numbers and outputs the result.

inlet 1: real value a
inlet 2: imaginary value a
inlet 3: real value b
inlet 4: imaginary value b
outlet 1: real sum
outlet 2: imaginary sum
argument 1: real value b
argument 2: imaginary value b

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[ cmplxdiv~ ] Complex Division
Performs complex division and outputs the result.

inlet 1: real numerator
inlet 2: imaginary numerator
inlet 3: real denominator
inlet 4: imaginary denominator
outlet 1: real result
outlet 2: imaginary result
argument 1: real denominator
argument 2: imaginary denominator

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[ cmplxmult~ ] Complex Multiplication
Multiplies two complex numbers and outputs the result.

inlet 1: real factor a
inlet 2: imaginary factor a
inlet 3: real factor b
inlet 4: imaginary factor b
outlet 1: real product
outlet 2: imaginary product
argument 1: real factor b
argument 2: imaginary factor b

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[ cmplxsqrt~ ] Complex Square Root
Calculates the square root of a complex number and outputs the result.

inlet 1: real value
inlet 2: imaginary value
outlet 1: real result
outlet 2: imaginary result

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[ cmplxsub~ ] Complex Subtraction
Subtracts one complex number form another and outputs the difference.

inlet 1: real minuend
inlet 2: imaginary minuend
inlet 3: real subtrahend
inlet 4: imaginary subtrahend
outlet 1: real difference
outlet 2: imaginary difference
argument 1: real subtrahend
argument 2: imaginary subtrahend

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[ countwrap ] Counter Wrap
Counts between minimum and maximum limits using an arbitrary increment value and wraps overflow back into counting range.

inlet 1: bang
inlet 2: current count
inlet 3: increment value
inlet 4: minimum value
inlet 5: maximum value
outlet: count value
1 argument: increment
2 arguments: minimum, maximum
3 arguments: increment, minimum, maximum
4 arguments: count, increment, minimum, maximum

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[ ctltosig~ ] Control to Signal
Scales values from control range (0 to 1) to signal range (-1 to 1).

inlet: control values
outlet: signal values

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[ dbtoamp~ ] Decibels to Amplitude
Converts dB-FS decibel values to amplitude values.

inlet: decibels
outlet: amplitude

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[ dbtomag~ ] Decibels to Magnitude
Converts dB-FS decibel values to magnitude values.

inlet 1: decibels
inlet 2: overlap factor
outlet: magnitude
argument: overlap factor

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[ degtorad~ ] Degrees to Radians
Converts degrees to radians.

inlet: degrees
outlet: radians

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[ degtoturn~ ] Degrees to Turns
Converts degrees to turns.

inlet: degrees
outlet: turns

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[ dspbang~ ] DSP Bang
Outputs a bang when DSP is turned on or when the DSP chain is reconstructed.

outlet: bang

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[ freqsieve~ ] Frequency Sieve
Assigns spectral frequency data to its proper bins based on frequency and magnitude. The frequency of greatest magnitude for each bin is selected and all other frequencies are ignored. An optional "unused" argument causes the object to output the ignored data.

inlet 1: magnitude
inlet 2: frequency
inlet 3: overlap factor
outlet 1: magnitude
outlet 2: frequency
1 argument: "unused" or overlap factor
2 arguments: "unused" and overlap factor

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[ freqtocar~ ] Frequency to Cartesian
Converts magnitude and frequency pairs to cartesian coordinates.

inlet 1: magnitude
inlet 2: frequency
inlet 3: overlap factor
outlet 1: real values
outlet 2: imaginary values
argument: overlap factor

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[ freqtophase~ ] Frequency to Phase
Converts frequency values to phase values for each bin of spectral data.

inlet 1: frequency
inlet 2: overlap factor
outlet: phase (-pi to pi)
argument: overlap factor

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[ freqtopolar~ ] Frequency to Polar
Converts magnitude and frequency pairs to polar coordinates.

inlet 1: magnitude
inlet 2: frequency
inlet 3: overlap factor
outlet 1: magnitude
outlet 2: phase (-pi to pi)
argument: overlap factor

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[ fundfreq~ ] Fundamental Frequency
Finds the fundamental frequency of greatest magnitude within a specified frequency range.

inlet 1: magnitude data
inlet 2: phase data
inlet 3: lower frequency limit
inlet 4: upper frequency limit
inlet 5: overlap factor
outlet: frequency
arguments: low freq, high freq, overlap factor

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[ harmprod~ ] Harmonic Product Spectrum
Calculates the harmonic product spectrum of an input spectrum. Default harmonic product spectrum uses 4 harmonics (i.e. 4x downsampling)

inlet: raw spectrum
outlet: harmonic product spectrum
argument: number of harmonics
message: "set ___" (harmonics)

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[ magtoamp~ ] Magnitude to Amplitude
Converts magnitude values to amplitude values.

inlet 1: magnitude
inlet 2: overlap factor
outlet: amplitude
argument: overlap factor

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[ magtodb~ ] Magnitude to Decibels
Converts magnitude values to dB-FS decibel values.

inlet 1: magnitude
inlet 2: overlap factor
outlet: decibels
argument: overlap factor

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[ magtrim~ ] Magnitude Trim
Zeroes spectral data outside of a specified magnitude range.

inlet 1: spectral data a
inlet 2: spectral data b
inlet 3: lower magnitude value
inlet 4: upper magnitude value
outlet 1: trimmed data a
outlet 2: trimmed data b
arguments: lower magnitude, upper magnitude

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[ monitor~ ] Monitor
Samples a signal and outputs a float every 20 milliseconds.

inlet: signal
outlet: float

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[ oscbank~ ] Oscillator Bank
Generates window-size/2 sinusoids based on input magnitude and frequency pairs. Magnitude and frequency changes are linearly interpolated between block boundaries.

inlet 1: magnitude data
inlet 2: frequency data
inlet 3: overlap factor
outlet: sinusoids

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[ pafft~ ] Phase Aligned FFT
Applies a window function then rotates the signal vector before performing a forward real fast fourier transform.

inlet 1: audio signal
inlet 2: rotation amount in samples
outlet 1: real values
outlet 2: imaginary values
argument: array_name (window array)
message: "set array_name"

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[ paifft~ ] Phase Aligned IFFT
Performs a backward real fast fourier transform then rotates the signal vector, applies a window function, and normalizes output.

inlet 1: real values
inlet 2: imaginary values
inlet 3: rotation amount in samples
outlet: audio signal
argument: array_name (window array)
message: "set array_name"

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[ partconv~ ] Partitioned Convolution
Performs partitioned convolution using cartesian coordinates with a convolution kernel stored in an external array.

inlet 1: real values
inlet 2: imaginary values
outlet 1: convolved real values
outlet 2: convolved imaginary values
message: "set kernel_array_name"
argument: kernel_array_name

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[ peaks~ ] Peaks
Finds peaks in inlet 1 spectral data, outputs peak values and associated data from inlet 2. Optionally detects an arbitrary number of highest peaks.

inlet 1: spectral data a
inlet 2: spectral data b
inlet 3: number of peaks
outlet 1: data a peaks
outlet 2: associated data b
argument: number of peaks

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[ phaseaccum~ ] Phase Accumulate
Calculates running sums of successive FFT frame phases for each bin.

inlet: spectral phase data
outlet: accumulated phase data

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[ phasedelta~ ] Phase Delta
Calculates phase deviation between successive FFT frames for each bin.

inlet: spectral phase data
outlet: phase delta data

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[ phasetofreq~ ] Phase to Frequency
Converts phase values to frequency values for each bin of spectral data.

inlet 1: frequency
inlet 2: overlap factor
outlet: phase (-pi to pi)
argument: overlap factor

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[ piwrap~ ] Pi Wrap
Wraps a signal between -pi and pi.

inlet 1: phase
outlet: wrapped phase

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[ polartocar~ ] Polar to Cartesian
Converts polar coordinates to cartesian coordinates.

inlet 1: magnitude
inlet 2: phase
outlet 1: real value
outlet 2: imaginary value

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[ polartofreq~ ] Polar to Frequency
Converts polar coordinates to magnitude and frequency pairs.

inlet 1: magnitude
inlet 2: phase
inlet 3: overlap factor
outlet 1: magnitude
outlet 2: frequency
argument: overlap factor

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[ radtodeg~ ] Radians to Degrees
Converts radians to degrees.

inlet: radians
outlet: degrees

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[ radtoturn~ ] Radians to Turns
Converts radians to turns.

inlet: radians
outlet: turns

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[ recip~ ] Reciprocal
Calculates reciprocal values.

inlet: signal
outlet: reciprocal

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[ rgbtable ] RGB Table
Outputs red, green, and blue values between 0 and 1 based on an input value between 0 and 1, according to the selected color scheme (default RGB).

inlet 1: float
outlet 1: red float
outlet 2: green float
outlet 3: blue float
argument: color scheme
message: color scheme

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[ rotate~ ] Rotate
Rotates a signal vector by an arbitrary number of samples.

inlet 1: signal vector
inlet 2: rotation amount
outlet: rotated signal
argument: rotation amount

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[ rounder~ ] Rounder
Rounds signal values to arbitrary precision of up to 8 decimal places. Default is zero decimal places.

inlet 1: signal
inlet 2: precision
outlet: rounded signal
argument: precision

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[ scale~ ] Scale
Scales a signal from one range to another.

inlet 1: signal
inlet 2: input minimum
inlet 3: input maximum
inlet 4: output minimum
inlet 5: output maximum
outlet: scaled signal
arguments: in minimum, in maximum, out minimum, out maximum

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[ sigtoctl~ ] Signal to Control
Scales values from signal range (-1 to 1) to control range (0 to 1).

inlet: signal values
outlet: control values

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[ softclip~ ] Soft Clipping
Applies the polynomial waveshaping function: y[n] = ( 3x[n] / 2 ) - ( x[n]^3 / 2 )

inlet: signal
outlet: smoothly clipped signal

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[ tabindex~ ] Table Index
Writes signal values into a table at arbitrary locations and optionally clears the array at the start of each signal vector.

inlet 1: signal
inlet 2: sample index
arguments: array_name, clear
message: "clear x" (where x is 0 or 1; sets clear behavior)
message: "set array_name"
message: "bang" (redraws array)

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[ terminal ] Terminal
Sends messages to an instance of the operating system's command line shell and outputs the results.

inlet: commands
outlet: results

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[ trunc~ ] Truncate
Truncates signal values to arbitrary precision of up to 8 decimal places. Default is zero decimal places.

inlet 1: signal
inlet 2: precision
outlet: truncated signal
argument: precision

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[ turntodeg~ ] Turns to Degrees
Converts turns to degrees.

inlet: turns
outlet: degrees

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[ turntorad~ ] Turns to Radians
Converts turns to radians.

inlet: turns
outlet: radians

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[ valleys~ ] Valleys
Finds valleys in inlet 1 spectral data, outputs valley values and associated data from inlet 2. Optionally detects an arbitrary number of highest valleys.

inlet 1: spectral data a
inlet 2: spectral data b
inlet 3: number of valleys
outlet 1: data a valleys
outlet 2: associated data b
argument: number of valleys

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[ windower ] Windower
Writes normalized window functions into arrays.

inlet: control messages
arguments: array_name, window_type, parameter
message: "set array_name"
message: "window_type"
message: "window_type parameter"

window types: bartlett-hann, blackman, blackman-harris, blackman-nuttall, cosine, gaussian, hann, hanning, hann-poisson, hamming, kaiser, lanczos, nuttall, poisson, rectangle, sine, triangle, tukey

parametric windows: blackman, gaussian, hann-poisson, kaiser, poisson, tukey

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[ winfft~ ] Windowed FFT
Applies a window function then performs a real fast fourier transform.

inlet 1: audio signal
outlet 1: real values
outlet 2: imaginary values
argument: array_name (window array)
message: "set array_name"

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[ winifft~ ] Windowed IFFT
Performs a real inverse fast fourier transform then applies a window function and normalizes output.

inlet 1: real values
inlet 2: imaginary values
outlet: audio signal
argument: array_name (window array)
message: "set array_name"

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