Wavelets

Wavelet families()

pywt.families()

Returns a list of available built-in wavelet families. Currently the built-in families are:

• Haar (haar)
• Daubechies (db)
• Symlets (sym)
• Coiflets (coif)
• Biorthogonal (bior)
• Reverse biorthogonal (rbio)
• “Discrete” FIR approximation of Meyer wavelet (dmey)

Example:

>>> import pywt
>>> print pywt.families()
['haar', 'db', 'sym', 'coif', 'bior', 'rbio', 'dmey']

Built-in wavelets - wavelist()

pywt.wavelist([family])

The wavelist() function returns a list of names of the built-in wavelets.

If the family name is None then names of all the built-in wavelets are returned. Otherwise the function returns names of wavelets that belong to the given family.

Example:

>>> import pywt
>>> print pywt.wavelist('coif')
['coif1', 'coif2', 'coif3', 'coif4', 'coif5']

Custom user wavelets are also supported through the Wavelet object constructor as described below.

Wavelet object

class pywt.Wavelet(name[, filter_bank=None])

Describes properties of a wavelet identified by the specified wavelet name. In order to use a built-in wavelet the name parameter must be a valid wavelet name from the pywt.wavelist() list.

Custom Wavelet objects can be created by passing a user-defined filters set with the filter_bank parameter.

Parameters:

• name – Wavelet name
• filter_bank – Use a user supplied filter bank instead of a built-in Wavelet.

The filter bank object can be a list of four filters coefficients or an object with filter_bank attribute, which returns a list of such filters in the following order:

[dec_lo, dec_hi, rec_lo, rec_hi]

Wavelet objects can also be used as a base filter banks. See section on using custom wavelets for more information.

Example:

>>> import pywt
>>> wavelet = pywt.Wavelet('db1')

name

Wavelet name.

short_name

Short wavelet name.

dec_lo

Decomposition filter values.

dec_hi

Decomposition filter values.

rec_lo

Reconstruction filter values.

rec_hi

Reconstruction filter values.

dec_len

Decomposition filter length.

rec_len

Reconstruction filter length.

filter_bank

Returns filters list for the current wavelet in the following order:

[dec_lo, dec_hi, rec_lo, rec_hi]

inverse_filter_bank

Returns list of reverse wavelet filters coefficients. The mapping from the filter_coeffs list is as follows:

[rec_lo[::-1], rec_hi[::-1], dec_lo[::-1], dec_hi[::-1]]

short_family_name

Wavelet short family name

family_name

Wavelet family name

orthogonal

Set if wavelet is orthogonal

biorthogonal

Set if wavelet is biorthogonal

symmetry

asymmetric, near symmetric, symmetric

vanishing_moments_psi

Number of vanishing moments for the wavelet function

vanishing_moments_phi

Number of vanishing moments for the scaling function

Example:

>>> def format_array(arr):
...     return "[%s]" % ", ".join(["%.14f" % x for x in arr])

>>> import pywt
>>> wavelet = pywt.Wavelet('db1')
>>> print wavelet
Wavelet db1
  Family name:    Daubechies
  Short name:     db
  Filters length: 2
  Orthogonal:     True
  Biorthogonal:   True
  Symmetry:       asymmetric
>>> print format_array(wavelet.dec_lo), format_array(wavelet.dec_hi)
[0.70710678118655, 0.70710678118655] [-0.70710678118655, 0.70710678118655]
>>> print format_array(wavelet.rec_lo), format_array(wavelet.rec_hi)
[0.70710678118655, 0.70710678118655] [0.70710678118655, -0.70710678118655]

Approximating wavelet and scaling functions - Wavelet.wavefun()

Wavelet.wavefun(level)

Changed in version 0.2: The time (space) localisation of approximation function points was added.

The wavefun() method can be used to calculate approximations of scaling function (phi) and wavelet function (psi) at the given level of refinement.

For orthogonal wavelets returns approximations of scaling function and wavelet function with corresponding x-grid coordinates:

[phi, psi, x] = wavelet.wavefun(level)

Example:

>>> import pywt
>>> wavelet = pywt.Wavelet('db2')
>>> phi, psi, x = wavelet.wavefun(level=5)

For other (biorthogonal but not orthogonal) wavelets returns approximations of scaling and wavelet function both for decomposition and reconstruction and corresponding x-grid coordinates:

[phi_d, psi_d, phi_r, psi_r, x] = wavelet.wavefun(level)

Example:

>>> import pywt
>>> wavelet = pywt.Wavelet('bior3.5')
>>> phi_d, psi_d, phi_r, psi_r, x = wavelet.wavefun(level=5)

See also

You can find live examples of wavefun() usage and images of all the built-in wavelets on the Wavelet Properties Browser page.

Using custom wavelets

PyWavelets comes with a long list of the most popular wavelets built-in and ready to use. If you need to use a specific wavelet which is not included in the list it is very easy to do so. Just pass a list of four filters or an object with a filter_bank attribute as a filter_bank argument to the Wavelet constructor.

The filters list, either in a form of a simple Python list or returned via the filter_bank attribute, must be in the following order:

• lowpass decomposition filter
• highpass decomposition filter
• lowpass reconstruction filter
• highpass reconstruction filter

just as for the filter_bank attribute of the Wavelet class.

The Wavelet object created in this way is a standard Wavelet instance.

The following example illustrates the way of creating custom Wavelet objects from plain Python lists of filter coefficients and a filter bank-like objects.

Example:

>>> import pywt, math
>>> c = math.sqrt(2)/2
>>> dec_lo, dec_hi, rec_lo, rec_hi = [c, c], [-c, c], [c, c], [c, -c]
>>> filter_bank = [dec_lo, dec_hi, rec_lo, rec_hi]
>>> myWavelet = pywt.Wavelet(name="myHaarWavelet", filter_bank=filter_bank)
>>>
>>> class HaarFilterBank(object):
...     @property
...     def filter_bank(self):
...         c = math.sqrt(2)/2
...         dec_lo, dec_hi, rec_lo, rec_hi = [c, c], [-c, c], [c, c], [c, -c]
...         return [dec_lo, dec_hi, rec_lo, rec_hi]
>>> filter_bank = HaarFilterBank()
>>> myOtherWavelet = pywt.Wavelet(name="myHaarWavelet", filter_bank=filter_bank)