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#data-analysis #data-science #scientific #signal-processing #wavelet-transform #wavelets

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README

This library is no longer actively maintained.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

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

CDN

Put the following script tag ` 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:
<pre><code class="lang-javascript">console.log(wt.Modes.modes); // expected output: Array [&#39;zero&#39;, &#39;constant&#39;, &#39;symmetric&#39;, &#39;periodic&#39;, &#39;smooth&#39;, &#39;reflect&#39;, &#39;antisymmetric&#39;]</code></pre>
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)
  - 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.
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
<pre><code class="lang-javascript">var coeffs = wt.dwt([1, 2, 3, 4], &quot;haar&quot;);
console.log(coeffs); // expected output: Array [[2.1213203435596425, 4.9497474683058326], [-0.7071067811865475, -0.7071067811865475]]</code></pre>
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
<pre><code class="lang-javascript">var coeffs = wt.wavedec([1, 2, 3, 4], &quot;haar&quot;);
console.log(coeffs); // expected output: Array [[4.999999999999999], [-1.9999999999999993], [-0.7071067811865475, -0.7071067811865475]]</code></pre>

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. 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.


Return

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


Example
<pre><code class="lang-javascript">var rec = wt.idwt(   [(1 + 2) / Math.SQRT2, (3 + 4) / Math.SQRT2],   [(1 - 2) / Math.SQRT2, (3 - 4) / Math.SQRT2],   &quot;haar&quot; );
console.log(rec); // expected output: Array [0.9999999999999999, 1.9999999999999996, 2.9999999999999996, 3.9999999999999996]</code></pre>

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
<pre><code class="lang-javascript">var data = wt.waverec([[5], [-2], [-1 / Math.SQRT2, -1 / Math.SQRT2]], &quot;haar&quot;);
console.log(data); // expected output: Array [0.9999999999999999, 1.9999999999999996, 2.999999999999999, 3.999999999999999]</code></pre>

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
<pre><code class="lang-javascript">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</code></pre>
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
<pre><code class="lang-javascript">var maxLevel = wt.maxLevel(4, &quot;haar&quot;);
console.log(maxLevel); // expected output: 2</code></pre>
<pre><code class="lang-javascript">var maxLevel = wt.maxLevel(1024, &quot;haar&quot;);
console.log(maxLevel); // expected output: 10</code></pre>
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
<pre><code class="lang-javascript">var pad = wt.pad([42, 51], [2, 1], &quot;zero&quot;);
console.log(pad); // expected output: Array [0, 0, 42, 51, 0]</code></pre>
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