# -*- coding: utf-8 -*-
from . import Filter
import numpy as np
from math import pi
[docs]class Simoncelli(Filter):
r"""
Simoncelli Filterbank
Inherits its methods from Filters
This function create a parseval filterbank of :math:`2`.
The low-pass filter is defined by a function :math:`f_l(x)`.
.. math:: f_{l}=\begin{cases} 1 & \mbox{if }x\leq a\\ \cos\left(\frac{\pi}{2}\frac{\log\left(\frac{x}{2}\right)}{\log(2)}\right) & \mbox{if }a<x\leq2a\\ 0 & \mbox{if }x>2a \end{cases}
The high pass filter is is adaptated to obtain a tight frame.
Parameters
----------
G : Graph
a : float
See equation above for this parameter
The spectrum is scaled between 0 and 2 (default = 2/3)
Returns
-------
out : Simoncelli
Examples
--------
>>> from pygsp import graphs, filters
>>> G = graphs.Logo()
>>> F = filters.Simoncelli(G)
"""
def __init__(self, G, a=2./3, **kwargs):
super(Simoncelli, self).__init__(G, **kwargs)
g = [lambda x: simoncelli(x * (2./G.lmax), a)]
g.append(lambda x: np.real(np.sqrt(1 -
(simoncelli(x*(2./G.lmax), a))
** 2)))
self.g = g
def simoncelli(val, a):
y = np.empty(np.shape(val))
l1 = a
l2 = 2 * a
r1ind = (val >= 0) * (val < l1)
r2ind = (val >= l1) * (val < l2)
r3ind = (val >= l2)
y[r1ind] = 1
y[r2ind] = np.cos(pi/2 * np.log(val[r2ind]/float(a)) / np.log(2))
y[r3ind] = 0
return y