This library is no longer actively maintained. This means that no new functionality or documentation is added.

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.

• Run npm install discrete-wavelets
• Add an import to the npm package import wt from 'discrete-wavelets';
• Then you can use the library in your code.

• Put the following script tag <script src="https://cdn.jsdelivr.net/npm/discrete-wavelets@5/dist/discrete-wavelets.umd.min.js"></script> in the head of your HTML file.
• Then you can use the library in your code.

The library uses the following types:

• PaddingMode: Signal extension modes.
• Wavelets: Wavelet bases.

The following values for PaddingMode are supported at the moment:

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']

The following Wavelet types are supported at the moment:

The library offers the following functions:

• Discrete Wavelet Transform (DWT)
  • dwt: Single level Discrete Wavelet Transform.
  • wavedec: 1D wavelet decomposition. Transforms data by calculating coefficients from input data.
• Inverse Discrete Wavelet Transform (IDWT)
  • idwt: Single level inverse Discrete Wavelet Transform.
  • waverec: 1D wavelet reconstruction. Inverses a transform by calculating input data from coefficients.
• Other
  • energy: Calculates the energy as sum of squares of an array of data or coefficients.
  • maxLevel: Determines the maximum level of useful decomposition.
  • pad: Extends a signal with a given padding mode.

Single level Discrete Wavelet Transform.

• data (number[]): Input data.
• wavelet (Wavelet): Wavelet to use.
• mode (PaddingMode): Signal extension mode. Defaults to 'symmetric'.

coeffs (number[][]): Approximation and detail coefficients as result of the transform.

var coeffs = wt.dwt([1, 2, 3, 4], "haar");

console.log(coeffs);
// expected output: Array [[2.1213203435596425, 4.9497474683058326], [-0.7071067811865475, -0.7071067811865475]]

1D wavelet decomposition. Transforms data by calculating coefficients from input data.

• 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.

coeffs (number[][]): Coefficients as result of the transform.

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]]

Single level inverse Discrete Wavelet Transform.

• approx (number[]): Approximation coefficients. If undefined, it will be set to an array of zeros with length equal to the detail coefficients.
• detail (number[]): Detail coefficients. If undefined, it will be set to an array of zeros with length equal to the approximation coefficients.
• wavelet (Wavelet): Wavelet to use.

rec (number[]): Approximation coefficients of previous level of transform.

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]

1D wavelet reconstruction. Inverses a transform by calculating input data from coefficients.

• coeffs (number[][]): Coefficients as result of a transform.
• wavelet (Wavelet): Wavelet to use.

data (number[]): Input data as result of the inverse transform.

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]

Calculates the energy as sum of squares of an array of data or coefficients.

• values (number[] | number[][]): Array of data or coefficients.

energy (number): Energy of values as the sum of squares.

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

Determines the maximum level of useful decomposition.

• dataLength (number): Length of input data.
• wavelet (Wavelet): Wavelet to use.

maxLevel (number): Maximum useful level of decomposition.

var maxLevel = wt.maxLevel(4, "haar");

console.log(maxLevel);
// expected output: 2

var maxLevel = wt.maxLevel(1024, "haar");

console.log(maxLevel);
// expected output: 10

Extends a signal with a given padding mode.

• data (number[]): Input data.
• padWidths ([number, number]): Widths of padding at front and back.
• mode (PaddingMode): Signal extension mode.

pad (number[]): Data with padding.

var pad = wt.pad([42, 51], [2, 1], "zero");

console.log(pad);
// expected output: Array [0, 0, 42, 51, 0]

• npm install: Install dependencies
• npm test: Run test suite
• npm start: Run npm 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