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Implements the Sigma Transform in C++
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Contents
This repository shows an exemplary implementation of the 'SigmaTransform', as defined in the thesis 'Quantum Frames and Uncertainty Principles arising from Symplectomorphisms', written in C/C++.
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, Wavelet Transform,Curvelet Transform, etc., differing only by single paramater - the 'spectral diffeomorphism'.
The code was compiled and tested with g++ (GCC) 4.8.1, on Windows 7 and g++ (Debian 4.7.2-5) 4.7.2 on Debian Linux, each on a 64 Bit machine, and uses the C++11 standard, as well as the FFTW library (http://fftw.org/), which should be installed prior to compilation. For Windows, a current 64 Bit shared-library version of FFTW3 (libfftw3-3.dll) is provided in the subdirectory ./FFTW. On a Linux machine, the library should be installedvia a package manager, e.g. using
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depending on your distribution, or compiled from scratch using the --enable-threads flag.
Usage
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Perform a STFT on a signal 'f'
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Perform a 1D Wavelet Transform on a signal 'f'
Perform a SIM(2)-Transform on a 2D signal 'f'
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Documentation
A HTML Documentation, generated by Doxygen (http://www.doxygen.nl), may be found int ./SigmaTransform/doc and the examples
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located in the ./Examples subdirectory show how to use the implementation, along with some special cases. The provided makefile should compile and link all examples - on Windows as well as Linux with the appropriate tools and libraries installed -, as well as the Code for the SigmaTransform itself. The binaries will be put into the subdirectory ./bin.