Signal Extension Modes

Import pywt first

>>> import pywt

>>> def format_array(a):
...     """Consistent array representation across different systems"""
...     import numpy
...     a = numpy.where(numpy.abs(a) < 1e-5, 0, a)
...     return numpy.array2string(a, precision=5, separator=' ', suppress_small=True)

List of available signal extension modes:

>>> print pywt.MODES.modes
['zpd', 'cpd', 'sym', 'ppd', 'sp1', 'per']

Test that dwt() and idwt() can be performed using every mode:

>>> x = [1,2,1,5,-1,8,4,6]
>>> for mode in pywt.MODES.modes:
...     cA, cD = pywt.dwt(x, 'db2', mode)
...     print "Mode:", mode
...     print "cA:", format_array(cA)
...     print "cD:", format_array(cD)
...     print "Reconstruction:", pywt.idwt(cA, cD, 'db2', mode)
Mode: zpd
cA: [-0.03468  1.73309  3.40612  6.32929  6.95095]
cD: [-0.12941 -2.156   -5.95035 -1.21545 -1.8625 ]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: cpd
cA: [ 1.2848   1.73309  3.40612  6.32929  7.51936]
cD: [-0.48296 -2.156   -5.95035 -1.21545  0.25882]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: sym
cA: [ 1.76777  1.73309  3.40612  6.32929  7.77817]
cD: [-0.61237 -2.156   -5.95035 -1.21545  1.22474]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: ppd
cA: [ 6.91627  1.73309  3.40612  6.32929  6.91627]
cD: [-1.99191 -2.156   -5.95035 -1.21545 -1.99191]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: sp1
cA: [-0.51764  1.73309  3.40612  6.32929  7.45001]
cD: [ 0.      -2.156   -5.95035 -1.21545  0.     ]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: per
cA: [ 4.05317  3.05257  2.85381  8.42522]
cD: [ 0.18947  4.18258  4.33738  2.60428]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]

Invalid mode name should rise a ValueError:

>>> pywt.dwt([1,2,3,4], 'db2', 'invalid')
Traceback (most recent call last):
...
ValueError: Unknown mode name 'invalid'.

You can also refer to modes via MODES class attributes:

>>> for mode_name in ['zpd', 'cpd', 'sym', 'ppd', 'sp1', 'per']:
...     mode = getattr(pywt.MODES, mode_name)
...     cA, cD = pywt.dwt([1,2,1,5,-1,8,4,6], 'db2', mode)
...     print "Mode:", mode, "(%s)" % mode_name
...     print "cA:", format_array(cA)
...     print "cD:", format_array(cD)
...     print "Reconstruction:", pywt.idwt(cA, cD, 'db2', mode)
Mode: 0 (zpd)
cA: [-0.03468  1.73309  3.40612  6.32929  6.95095]
cD: [-0.12941 -2.156   -5.95035 -1.21545 -1.8625 ]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: 2 (cpd)
cA: [ 1.2848   1.73309  3.40612  6.32929  7.51936]
cD: [-0.48296 -2.156   -5.95035 -1.21545  0.25882]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: 1 (sym)
cA: [ 1.76777  1.73309  3.40612  6.32929  7.77817]
cD: [-0.61237 -2.156   -5.95035 -1.21545  1.22474]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: 4 (ppd)
cA: [ 6.91627  1.73309  3.40612  6.32929  6.91627]
cD: [-1.99191 -2.156   -5.95035 -1.21545 -1.99191]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: 3 (sp1)
cA: [-0.51764  1.73309  3.40612  6.32929  7.45001]
cD: [ 0.      -2.156   -5.95035 -1.21545  0.     ]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]
Mode: 5 (per)
cA: [ 4.05317  3.05257  2.85381  8.42522]
cD: [ 0.18947  4.18258  4.33738  2.60428]
Reconstruction: [ 1.  2.  1.  5. -1.  8.  4.  6.]

Some invalid mode values:

>>> pywt.dwt(x, 'db2', -1)
Traceback (most recent call last):
...
ValueError: Invalid mode.
>>> pywt.dwt(x, 'db2', 7)
Traceback (most recent call last):
...
ValueError: Invalid mode.

>>> pywt.dwt(x, 'db2', None)
Traceback (most recent call last):
...
TypeError: expected string or Unicode object, NoneType found

The default mode is sym:

>>> cA, cD = pywt.dwt(x, 'db2')
>>> print cA
[ 1.76776695  1.73309178  3.40612438  6.32928585  7.77817459]
>>> print cD
[-0.61237244 -2.15599552 -5.95034847 -1.21545369  1.22474487]
>>> print pywt.idwt(cA, cD, 'db2')
[ 1.  2.  1.  5. -1.  8.  4.  6.]

And using a keyword argument:

>>> cA, cD = pywt.dwt(x, 'db2', mode='sym')
>>> print cA
[ 1.76776695  1.73309178  3.40612438  6.32928585  7.77817459]
>>> print cD
[-0.61237244 -2.15599552 -5.95034847 -1.21545369  1.22474487]
>>> print pywt.idwt(cA, cD, 'db2')
[ 1.  2.  1.  5. -1.  8.  4.  6.]