initial

Author: dl

Example1D_STFT.py

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+#!/usr/bin/python -u
+
+# the needed extern modules
+import numpy as np
+
+# own module
+import sigmatransform as st
+
+# setup
+np.set_printoptions(precision=2,edgeitems=10,linewidth=120)
+
+# the channels
+Fs = 143000;
+chan = np.linspace(-Fs/2.0,Fs/2.0,400);
+
+# the Gaussian window
+def win(x):
+    return np.exp(-np.pi* ( x / Fs * 400 / 16.0 )**2 );
+
+# the (trivial) diffeomorphism (for STFT)
+def sig(x): return x;
+
+# the signal
+f = np.loadtxt("bat.asc");
+
+# get an instance
+STFT = st.SigmaTransform( 
+    sig ,   # the diffeomorphism handle 
+    win ,   # the window handle
+    Fs  ,   # the sampling Frequency
+    chan    # the channels in warped Fourier domain
+);
+
+# analyze the signal f (coeff is stored internally, so no need to capture "coeff" right now)...
+STFT.analyze( f );
+# ...and get coeffs
+co = STFT.coeff;
+
+# try to reconstruct "f" from its coefficients (without dual frame, so depends on the chosen channels)
+# and store in "recVec"
+recVec = STFT.synthesize().rec;
+
+# plot the modulus of the ceofficients
+STFT.plotCoeff();
+
+# apply multiplier...
+STFT.analyze(f).applyMaskFunc(lambda x,y : (x>.5)*(y>0)+.5 ).synthesize();
+recMasked = STFT.rec;
+STFT.plotCoeff();
+
+# ...or short:
+recMasked = st.SigmaTransform(
+    lambda x : x,
+    lambda x : np.exp(-np.pi*(x/Fs*400.0/16.0)**2),
+    143000, 
+    np.linspace(-Fs/2.0,Fs/2.0,400)
+).multiplier(
+    np.loadtxt("bat.asc"),
+    lambda x,y : (x < .5)*(y<0) + .2
+).plotCoeff();

Example1D_Wavelet.py

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+#!/usr/bin/python -u
+
+# the needed extern modules
+import numpy as np
+
+# own module
+import sigmatransform as st
+
+# setup
+np.set_printoptions(precision=2,edgeitems=10,linewidth=120)
+numsteps = 400.0;
+winwidth = 4.0;
+
+# the channels
+Fs = 143000.0;
+chan = np.linspace( np.log2(Fs*0.005) , np.log2(Fs/2.0*1.1) , numsteps );
+
+# the diffeomorphism
+def sig(x): 
+    return np.log2( x * (x>0.0) );
+
+# the adapted Gaussian window in warped domain
+def win(x):
+    return np.exp(-np.pi*( x / sig(Fs) * numsteps / winwidth )**2 );
+
+# the signal
+f = np.loadtxt("bat.asc");
+
+# get an instance
+Wavelet = st.SigmaTransform( 
+    sig ,   # the diffeomorphism handle 
+    win ,   # the window handle
+    Fs  ,   # the sampling Frequency
+    chan    # the channels in warped Fourier domain
+);
+
+# analyze the signal f (coeff is stored internally, so no need to capture "coeff" right now)...
+Wavelet.analyze( f );
+# ...and get coeffs
+co = Wavelet.coeff;
+
+# try to reconstruct "f" from its coefficients (without dual frame, so depends on the chosen channels)
+# and store in "recVec"
+recVec = Wavelet.synthesize().rec;
+
+# plot the modulus of the ceofficients
+Wavelet.plotCoeff();
+
+# apply Wavelet-Multiplier...
+Wavelet.analyze(f).applyMaskFunc(lambda x,y : (x>.5)*(y>10)+.5 ).synthesize();
+#recMasked = Wavelet.rec;
+Wavelet.plotCoeff();
+
+# ...or, as a "one-liner":
+recMasked = st.SigmaTransform(
+    lambda x : np.log2( x * (x>0.0) ),
+    lambda x : np.exp(-np.pi*( x / sig(Fs) * 400.0 / 4.0 )**2 ),
+    143000, 
+    np.linspace( np.log2(Fs*0.005) , np.log2(Fs/2.0*1.1) , 400 )
+).multiplier(
+    np.loadtxt("bat.asc"),
+    lambda x,y : (x < .5)*(y>10) + .2
+).plotCoeff();

README.md

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+
+# SigmaTransform-Python
+Implements the Sigma Transform in Python
+
+## Contents
+- [General Information](#general-information)
+- [Usage and Examples](#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
+
+# 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
+```python
+import sigmatransform as st
+...
+# define diffeomorphism
+sig = lambda x : x;
+# get an instance
+STFT = st.SigmaTransform( 
+    sig ,   # the diffeomorphism handle 
+    win ,   # the window handle
+    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
+```python
+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
+    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.