Cwt

demo/coeffs.py

@@ -0,0 +1,79 @@
+import pywt, numpy, pylab, time
+import sample_data
+
+interpolation = 'nearest' #'bilinear'
+cmap = pylab.cm.jet
+
+absolute_values = 0
+normalize = 0
+
+scales = range(4, 129, 2)
+sample = 1
+
+if sample == 1:
+    x = numpy.linspace(-300, 1300, 1024*1)
+    data = 2*numpy.sin(2*numpy.pi/4 * x) * numpy.exp(-(x-400)**2/(2*300**2)) + \
+           numpy.sin(2*numpy.pi/32*x) * numpy.exp(-(x-700)**2/(2*100**2)) + \
+           numpy.sin(2*numpy.pi/32 * (x/(1+x/1000)) )
+elif sample == 2:
+    data = sample_data.cuspamax
+    data = data
+    x = range(len(data))
+elif sample == 3:
+    data = sample_data.linchirp
+    x = range(len(data))
+elif sample == 4:
+    data = sample_data.ecg
+    x = range(len(data))
+
+wavelets = ['db1', 'sym5', 'coif3', 'bior1.5', 'bior3.3', 'bior4.4'][:2]
+#, pywt.cwt.morlet(len(data)), pywt.cwt.mexican_hat(len(data))]#[:4]#[-1:]
+wavelets = [pywt.cwt.cmorlet(len(data)/4, 1.0, 1.0),
+            pywt.cwt.cmorlet(len(data)/4, 4.0, 1.0),
+            pywt.cwt.cmorlet(len(data)/4, 1.0, 4.0)]#, pywt.cwt.gauss1(len(data))] #, 'coif3', 'bior1.5', 'bior3.3', 'bior4.4', pywt.cwt.morlet(len(data)), pywt.cwt.mexican_hat(len(data))]#[:4]#[-1:]
+#wavelets = [pywt.cwt.morlet(len(data)), pywt.cwt.mexican_hat(len(data)), pywt.cwt.gauss1(len(data)), pywt.cwt.gauss2(len(data)), pywt.cwt.gauss3(len(data))]
+#wavelets = ['cmorlet2-2', 'cmorlet1-1']
+#wavelets = ['mexican_hat', 'cmorlet2-2', 'cmorlet1-1']
+#wavelets = ['cfbsp4-0.7-1', pywt.cwt.cfbsp(len(data), 4, 0.7, 1)]#, 'cmorlet1-1']
+#wavelets = [pywt.cwt.cmorlet(2**8, 2, 2)]
+
+for name in ['mexican_hat', 'morlet', 'gauss1', 'gauss2', 'gauss3', 'cfbsp1-1-1', 'cmorlet1-1', 'cshannon1-1']:
+    print name,
+    t = time.clock()
+    #pywt.cwt.CWavelet(name).wavefun(19)
+    print time.clock() - t
+
+#p,x = pywt.cwt.CWavelet('cfbsp1-1-1').wavefun()
+#pylab.plot(x,p.real)
+#pylab.plot(x,p.imag)
+#pylab.show()
+
+
+for wavelet in wavelets:
+    #print wavelet
+    pylab.figure()
+    pylab.subplot(3,1,1)
+    t = time.clock()
+    print len(data), len(scales)
+    c = pywt.cwt.cwt(data, wavelet=wavelet, scales=scales, data_step=x[1]-x[0], precision=16)
+    print "%.4f" % (time.clock()-t)
+
+    if absolute_values:
+        c = numpy.abs(numpy.asarray(c).real)
+    if normalize:
+        for y in c:
+            y *= 1.0 / max(abs(y.max()), abs(y.min()))
+
+    c = numpy.asarray(c).real
+    pylab.imshow(c, origin='image', interpolation=interpolation, aspect='auto', cmap=cmap)
+    pylab.subplot(3,1,2)
+    pylab.plot(x, data)
+    pylab.xlim(x[0], x[-1])
+
+    pylab.subplot(3,1,3)
+    for i in [j for j in (4, 16, 32, 64, 128) if j <= max(scales) and j in scales]:
+        pylab.plot(x, c[scales.index(i)], label= ("scale a = %d" % i))
+    pylab.legend()
+    pylab.xlim(x[0], x[-1])
+pylab.show()
+

demo/continuous.py

@@ -0,0 +1,7 @@
+import pywt
+import pywt.cwt as c
+import pylab
+
+psi, x = c.mexican_hat(1000)
+pylab.plot(x, psi)
+pylab.show()

demo/freq.py

@@ -0,0 +1,23 @@
+import pywt, numpy
+#, pylab, time
+import sample_data
+
+#interpolation = 'nearest' #'bilinear'
+#cmap = pylab.cm.jet
+
+from pywt.functions import centfrq, orthfilt
+print centfrq('db1', 8)
+print centfrq('db2', 8)
+print centfrq(pywt.cwt.morlet(256))
+print centfrq(pywt.cwt.mexican_hat(256))
+#print pywt.cwt.mexican_hat(256)[0]
+
+import pylab
+pylab.plot(*pywt.cwt.cgauss1(256)[::-1])
+pylab.show()
+
+#for i in pywt.wavelist():
+#    print "%s = %s" % (i.replace('.', '_'), centfrq(i, 8))
+
+
+#print orthfilt([1,2,3,4,5,6])

doc/cwt.rst

@@ -0,0 +1,51 @@
+Continuous Wavelet Transform (CWT)
+----------------------------------
+
+cwavelist()
+~~~~~~~~~~~
+
+
+.. _`CWavelet`:
+
+Continuous Wavelet - ``CWavelet``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+::
+
+    CWavelet(name, psi=None, properties={})
+
+
+Continuous Wavelet Transform with ``cwt``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+1D Continuous Wavelet Transform
+
+::
+
+    coeffs = cwt(data, wavelet, scales, data_step=1.0, precision=10)
+
+data
+  1D input data
+
+wavelet
+  Wavelet *name*, CWavelet_ object or Wavelet_ object.
+
+  For convenience, a pair of `(function_approximation, x_grid)` arrays can aslo
+  be used here::
+
+    coeffs cwt(data, (psi, x_grid), scales, data_step=1.0, precision=10)
+
+scales
+  A list of scales at which to perform the CWT.
+
+data_step
+  The distance between two neighbour points on the x-axis.
+
+precision
+ Applicable only when wavelet *name*, *CWavelet* object or *Wavelet* object is
+ passed as the *wavelet* parameter and is used to calculate the wavelet function
+ approximation.
+
+The function returns a list of coefficients arrays, one for every scale value
+in *scales*.
+

pywt/__init__.py

@@ -14,14 +14,17 @@
 from multilevel import *
 from multidim import *
 from wavelet_packets import *
+from functions import *
 import thresholding
+import cwt
 
 from release_details import version as __version__, author as __author__, license as __license__
 __all__ = []
 __all__ += _pywt.__all__
 __all__ += wavelet_packets.__all__
 __all__ += multilevel.__all__
 __all__ += multidim.__all__
-__all__ += ['thresholding']
+__all__ += functions.__all__
+__all__ += ['thresholding', 'cwt']
 
 del multilevel, multidim, wavelet_packets