# -*- coding: utf-8 -*-
import numpy as np
from . import Filter # prevent circular import in Python < 3.5
[docs]class HalfCosine(Filter):
r"""Design an half cosine filter bank (tight frame).
Parameters
----------
G : graph
Nf : int
Number of filters from 0 to lmax (default = 6)
Examples
--------
Filter bank's representation in Fourier and time (ring graph) domains.
>>> import matplotlib.pyplot as plt
>>> G = graphs.Ring(N=20)
>>> G.estimate_lmax()
>>> G.set_coordinates('line1D')
>>> g = filters.HalfCosine(G)
>>> s = g.localize(G.N // 2)
>>> fig, axes = plt.subplots(1, 2)
>>> g.plot(ax=axes[0])
>>> G.plot_signal(s, ax=axes[1])
"""
def __init__(self, G, Nf=6, **kwargs):
if Nf <= 2:
raise ValueError('The number of filters must be higher than 2.')
dila_fact = G.lmax * (3./(Nf - 2))
main_window = lambda x: np.multiply(np.multiply((.5 + .5*np.cos(2.*np.pi*(x/dila_fact - 1./2))), (x >= 0)), (x <= dila_fact))
g = []
for i in range(Nf):
g.append(lambda x, ind=i: main_window(x - dila_fact/3. * (ind - 2)))
super(HalfCosine, self).__init__(G, g, **kwargs)