Dft-Easy
===============================================
Discrete Fourrier Transform made easy

Example

``js
let data = [
[0.00, 1],
[0.25, 0],
[0.50, -1],
[0.75, 0],
[1.00, 1],
[1.25, 0],
[1.50, -1],
[1.75, 0],
]
`
`js
let dftResult = require("dft-easy")(data)
[
[frequency0, frequency0Magnitude, frequency0Phase],
[frequency1, frequency1Magnitude, frequency1Phase],
...
]
require("gnu-plot")().plot([ {data: dftResult} ])
`
`js
let dftResult = require("dft-easy")(data, {frequencies:{list:[0.5,1,2]}})
[
[ 0.5, 0.36..., 2.7... ],
[ 1, 0.91..., 2e-16 ],
[ 2, 0.02..., 5e-16 ]
]
`

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- Linear scale: demo/demo.js
- Logarithmic scale: demo/demo_dB.js

Methods

dft(data, options)

execute dft

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result formatted as :
`js
[
[frequency0, frequency0Magnitude, frequency0Phase],
[frequency1, frequency1Magnitude, frequency1Phase],
...
]
`

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Ordered data points formatted as :
`js
[
[sample0Time, sample0Amplitude],
[sample1Time, sample1Amplitude],
...
]
`

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Note that the object is cloned and therefore not modified.
If you want to read or optimize the calculation of default options, see dft.constructOptions().

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default: {}
There are 3 possibilities:
- provide an Array of frequencies in options.frequencies.list
- provide {min, max, number, logBase} parameters to generate this list (see default)
- provide some or none of these parameters. The rest will be infered from the data (see default)

#### options.frequencies.min
default: 1/(data[data.length-1][0]-data[0][0])
Maximum frequency of the dft
Default is calculated from data duration, because you need at least one full period to detect a certain frequency

#### options.frequencies.max
default: (1/) / 2
Minimum frequency of the dft
Default is calculated from the minimum time delta between every data point. Nyquist says that a frequency can only be correctly represented by a double sample frequency.

#### options.frequencies.number
default: 4096
Number of equally spaced points (at log options.frequencies.logBase)

#### options.frequencies.logBase
default: 10
Base of the logarithmic spacing of frequencies

#### options.frequencies.list
default: options.frequencies.number frequencies in [options.frequencies.min, options.frequencies.max], equally spaced in a logarithmic space of base options.frequencies.logBase>
Array of frequencies where the dft will calculate the Magnitude and Phase

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default: dft.windows.Taylor()
Function taking t from 0->1 and returning a multiplication factor.
Integral(window(t), 0, 1) should be equal to 1.
You can provide your own window function, or pick one from dft.windows :
`js
[
Box(),
Triangular(),
Welch(),
Hann(),
Hamming(),
Blackman(),
Nuttal(),
BlackmanNuttal(),
BlackmanHarris(),
FlatTop(),
Taylor({interpolationSteps:256, sidelobesNumber:4, sidelobesAttenuation:35/dB/}),
Tukey({alpha:.5})
]
`
Some have configurable parameters that are indicated with their defaults
Most of these come from wikipedia.org/wiki/Window_function

dft.constructOptions(data, options)

This is the method that fills all the options values that aren't provided with their defaults.
You should cache this object when calling the dft quickly or when you want the frequency list to be stable.
`js
let dftOptions = dft.constructOptions(dataChunks[0])
for(let i=0; i dft(dataChunks[i], dftOptions)
}
`

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Constructed options object

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See dft().

dft.peak(dftResult)

Utility to find Magnitude peak in dftResult

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[frequency, magnitude, phase]`

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Result returned from dft()