Discrete Wavelets
A Discrete Wavelet Transform (DWT) library for the web.
This library is well tested. Still, it may contain some errors. Therefore it is recommended to double check the results with another library such as PyWavelets. If you find any errors, please let me know by opening an issue or a pull request.
Importing this library
Node Modules
 Run
npm install discretewavelets
 Add an import to the npm package
import wt from 'discretewavelets';
 Then you can use the library in your code.
CDN
 Put the following script tag
<script src="https://cdn.jsdelivr.net/npm/discretewavelets@5/dist/discretewavelets.umd.min.js"></script>
in the head of your HTML file.  Then you can use the library in your code.
Types
The library uses the following types:
 PaddingMode: Signal extension modes.
 Wavelets: Wavelet bases.
PaddingMode
The following values for PaddingMode
are supported at the moment:
Name  Value  Description 

Zero Padding  'zero' 
Adding zeros. 
Constant Padding  'constant' 
Replication of border values. 
Symmetric Padding  'symmetric' 
Mirroring of samples. 
Reflect Padding  'reflect' 
Reflecting of samples. 
Periodic Padding  'periodic' 
Treating signal as a periodic one. 
Smooth Padding  'smooth' 
Signal extended as a straight line. 
Antisymmetric Padding  'antisymmetric' 
Mirroring and negation of samples. 
You can get a list of the supported signal extension modes:
console.log(wt.Modes.modes);
// expected output: Array ['zero', 'constant', 'symmetric', 'periodic', 'smooth', 'reflect', 'antisymmetric']
Wavelets
The following Wavelet
types are supported at the moment:
Wavelet  Aliases 

Daubechies 1 / Haar 
'db1' , 'D2' , 'haar'

Daubechies 2 
'db2' , 'D4'

Daubechies 3 
'db3' , 'D6'

Daubechies 4 
'db4' , 'D8'

Daubechies 5 
'db5' , 'D10'

Daubechies 6 
'db6' , 'D12'

Daubechies 7 
'db7' , 'D14'

Daubechies 8 
'db8' , 'D16'

Daubechies 9 
'db9' , 'D18'

Daubechies 10 
'db10' , 'D20'

API
The library offers the following functions:
 Discrete Wavelet Transform (DWT)
 Inverse Discrete Wavelet Transform (IDWT)
 Other
dwt
Single level Discrete Wavelet Transform.
Arguments

data
(number[]
): Input data. 
wavelet
(Wavelet
): Wavelet to use. 
mode
(PaddingMode
): Signal extension mode. Defaults to'symmetric'
.
Return
coeffs
(number[][]
): Approximation and detail coefficients as result of the transform.
Example
var coeffs = wt.dwt([1, 2, 3, 4], 'haar');
console.log(coeffs);
// expected output: Array [[2.1213203435596425, 4.9497474683058326], [0.7071067811865475, 0.7071067811865475]]
wavedec
1D wavelet decomposition. Transforms data by calculating coefficients from input data.
Arguments

data
(number[]
): Input data. 
wavelet
(Wavelet
): Wavelet to use. 
mode
(PaddingMode
): Signal extension mode. Defaults to'symmetric'
. 
level
(number
): Decomposition level. Defaults to level calculated by maxLevel function.
Return
coeffs
(number[][]
): Coefficients as result of the transform.
Example
var coeffs = wt.wavedec([1, 2, 3, 4], 'haar');
console.log(coeffs);
// expected output: Array [[4.999999999999999], [1.9999999999999993], [0.7071067811865475, 0.7071067811865475]]
Be aware that due to floating point imprecision the result diverges slightly from the analytical solution [[5], [2], [0.7071067811865475, 0.7071067811865475]]
idwt
Single level inverse Discrete Wavelet Transform.
Arguments

approx
(number[]
): Approximation coefficients. Ifundefined
, it will be set to an array of zeros with length equal to the detail coefficients. 
detail
(number[]
): Detail coefficients. Ifundefined
, it will be set to an array of zeros with length equal to the approximation coefficients. 
wavelet
(Wavelet
): Wavelet to use.
Return
rec
(number[]
): Approximation coefficients of previous level of transform.
Example
var rec = wt.idwt(
[(1 + 2) / Math.SQRT2, (3 + 4) / Math.SQRT2],
[(1  2) / Math.SQRT2, (3  4) / Math.SQRT2],
'haar'
);
console.log(rec);
// expected output: Array [0.9999999999999999, 1.9999999999999996, 2.9999999999999996, 3.9999999999999996]
Be aware that due to floating point imprecision the result diverges slightly from the analytical solution [1, 2, 3, 4]
waverec
1D wavelet reconstruction. Inverses a transform by calculating input data from coefficients.
Arguments

coeffs
(number[][]
): Coefficients as result of a transform. 
wavelet
(Wavelet
): Wavelet to use.
Return
data
(number[]
): Input data as result of the inverse transform.
Example
var data = wt.waverec(
[[5], [2], [1 / Math.SQRT2, 1 / Math.SQRT2]],
'haar'
);
console.log(data);
// expected output: Array [0.9999999999999999, 1.9999999999999996, 2.999999999999999, 3.999999999999999]
Be aware that due to floating point imprecision the result diverges slightly from the analytical solution [1, 2, 3, 4]
energy
Calculates the energy as sum of squares of an array of data or coefficients.
Argument

values
(number[]  number[][]
): Array of data or coefficients.
Return
energy
(number
): Energy of values as the sum of squares.
Examples
console.log(
wt.energy([1, 2, 6, 1])
);
// expected output: 42
console.log(
wt.energy([[5], [2], [1 / Math.SQRT2, 1 / Math.SQRT2]])
);
// expected output: 30
maxLevel
Determines the maximum level of useful decomposition.
Arguments

dataLength
(number
): Length of input data. 
wavelet
(Wavelet
): Wavelet to use.
Return
maxLevel
(number
): Maximum useful level of decomposition.
Examples
var maxLevel = wt.maxLevel(4, 'haar');
console.log(maxLevel);
// expected output: 2
var maxLevel = wt.maxLevel(1024, 'haar');
console.log(maxLevel);
// expected output: 10
pad
Extends a signal with a given padding mode.
Arguments

data
(number[]
): Input data. 
padWidths
([number, number]
): Widths of padding at front and back. 
mode
(PaddingMode
): Signal extension mode.
Return
pad
(number[]
): Data with padding.
Example
var pad = wt.pad([42, 51], [2, 1], 'zero');
console.log(pad);
// expected output: Array [0, 0, 42, 51, 0]
NPM scripts

npm install
: Install dependencies 
npm test
: Run test suite 
npm start
: Runnpm run build
in watch mode 
npm run test:watch
: Run test suite in interactive watch mode 
npm run test:prod
: Run linting and generate coverage 
npm run build
: Generate bundles and typings, create docs 
npm run lint
: Lints code
This library in action
An exemplary application with code using this library can be found at https://symmetronic.github.io/covid19dwtanalysis/
Related project
Symmetronic Scaleogram is a web component that allows to easily create a scaleogram visualization from wavelet coefficients.
Contributing
Pull requests are welcome! Please include new tests for your code and make sure that all tests succeed running npm test
.