Implements the Sigma Transform in JavaScript.
This repository shows an exemplary implementation of the "SigmaTransform", as defined in the thesis "Quantum Frames and Uncertainty Principles arising from Symplectomorphisms", written in JavaScript.
Note that this library is not intended to show maximal performance, but show the usability of the universal interface of the "Sigma Transform" to perform well-known signal processing transforms / algorithms like the Short-Time Fourier Transform and Wavelet Transform.
Currently, only the one- and two-dimensional SigmaTransform is implemented and utilizes the jsfft library from https://github.com/dntj/jsfft.
Clone this repository, or copy the files to a local folder.
Perform a Wavelet Transform on a signal "f" and get coefficients and reconstruction
// get SigmaTransform class
const st = require('./SigmaTransform.js');
// define a spectral diffeomorphism, e.g. logarithm for WaveletTransform
const sig = x => Math.log2(x*(x>0));
// define a window, e.g. a standard Gaussian (in the warped Domain)
const gauss = x => Math.exp(-Math.PI * x**2 );
// create WaveletTransform object
const WT = new st.SigmaTransform1D(
sig , // the diffeomorphism
gauss , // the window
Fs , // the sampling frequency
N , // the signal-size
chans // the channels in warped fourier domain
);
// compute WT of signal "f"...
WT.analyze( f );
// ...get coefficients
var coeff = WT.coeff;
// try to reconstruct (no dual windows involved) and get data
var rec = WT.synthesize().rec;The javascript files
Example1D_STFT.js
Example1D_Wavelet.js
Example2D_STFT.js
Example1D_SIM2.js
provide more elaborated usage examples and may be run with node.js via
node Example1D_STFT.js
node Example1D_Wavelet.js
node Example2D_STFT.js
node Example1D_SIM2.js