SigmaTransform-Python

Implements the Sigma Transform in Python

Contents

• General Information
• Usage and Examples

General information

This repository shows an exemplary implementation of the "SigmaTransform", as defined in the thesis "Quantum Frames and Uncertainty Principles arising from Symplectomorphisms", written in Python.

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-dimensional SigmaTransform is implemented and utilizes NumPy and Matplotlib.

Usage and Examples

Clone this repository, or copy the file "sigmatransform.py" to a local folder.

Usage

Perform a STFT on a signal "f" and save coefficients as numpy array

import sigmatransform as st
...
# define diffeomorphism
sig = lambda x : x;
# get an instance
STFT = st.SigmaTransform( 
    sig   , # the diffeomorphism handle 
    win   , # the window handle
    len(f), # the signal length
    Fs    , # the sampling Frequency
    chan    # the channels in warped Fourier domain
);
# analyze the signal "f", given as numpy array ...
STFT.analyze( f );
# ...and get coeffs, as numpy array
coeff = STFT.coeff;

Perform a Wavelet transform on a signal "f" and plot coefficients

import sigmatransform as st
...
# define diffeomorphism
sig = lambda x : np.log2(x*(x>0));
# get an instance
Wavelet = st.SigmaTransform( 
    sig   , # the diffeomorphism handle 
    win   , # the window handle
    len(f), # the signal length
    Fs    , # the sampling Frequency
    chan    # the channels in warped Fourier domain
);
# analyze the signal "f", given as numpy array ...
Wavelet.analyze( f );
# ... and plot coeffs
Wavelet.plotCoeff();

Examples

The python scripts

    Example1D_STFT.py
    Example1D_Wavelet.py

provide more elaborated usage examples.