# -*- coding: utf-8 -*-
# ######### COPYRIGHT #########
# Credits
# #######
#
# Copyright(c) 2015-2018
# ----------------------
#
# * `LabEx Archimède <http://labex-archimede.univ-amu.fr/>`_
# * `Laboratoire d'Informatique Fondamentale <http://www.lif.univ-mrs.fr/>`_
# (now `Laboratoire d'Informatique et Systèmes <http://www.lis-lab.fr/>`_)
# * `Institut de Mathématiques de Marseille <http://www.i2m.univ-amu.fr/>`_
# * `Université d'Aix-Marseille <http://www.univ-amu.fr/>`_
#
# This software is a port from LTFAT 2.1.0 :
# Copyright (C) 2005-2018 Peter L. Soendergaard <peter@sonderport.dk>.
#
# Contributors
# ------------
#
# * Denis Arrivault <contact.dev_AT_lis-lab.fr>
# * Florent Jaillet <contact.dev_AT_lis-lab.fr>
#
# Description
# -----------
#
# ltfatpy is a partial Python port of the
# `Large Time/Frequency Analysis Toolbox <http://ltfat.sourceforge.net/>`_,
# a MATLAB®/Octave toolbox for working with time-frequency analysis and
# synthesis.
#
# Version
# -------
#
# * ltfatpy version = 1.0.16
# * LTFAT version = 2.1.0
#
# Licence
# -------
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# ######### COPYRIGHT #########
"""Module of Canonical dual window calculation
Ported from ltfat_2.1.0/gabor/gabdual.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.gabor.dgtlength import dgtlength
from ltfatpy.gabor.gabframediag import gabframediag
from ltfatpy.sigproc.fir2long import fir2long
from ltfatpy.sigproc.long2fir import long2fir
from ltfatpy.comp.comp_gabdual_long import comp_gabdual_long
[docs]def gabdual(g, a, M, L=None):
"""Canonical dual window of Gabor frame
- Usage:
| ``gd = gabdual(g, a, M)``
| ``gd = gabdual(g, a, M, L)``
- Input parameters:
:param g: the gabor window.
:param int a: the length of time shift.
:param int M: the number of channels.
:param int L: the length of window. (optional)
:type g: numpy.ndarray or str or dict
- Output parameters:
:returns: the canonical dual window
:rtype: numpy.ndarray
``gabdual(g, a, M)`` computes the canonical dual window of the discrete
Gabor frame with window **g** and parameters **a**, **M**.
The window **g** may be a vector of numerical values, a text string or a
dictionary.
If the length of **g** is equal to **M**, then the input window is
assumed to be an FIR window. In this case, the canonical dual window also
has length of **M**. Otherwise the smallest possible transform length is
chosen as the window length.
``gabdual(g, a, M, L)`` returns a window that is the dual window for a
system of length **L**. Unless the dual window is a FIR window, the dual
window will have length **L**.
If :math:`a > M` then the dual window of the Gabor Riesz sequence with
window **g** and parameters **a** and **M** will be calculated.
- Example:
The following example shows the canonical dual window of the Gaussian
window.
>>> import matplotlib.pyplot as plt
>>> from ltfatpy import pgauss, gabdual
>>> a = 20
>>> M = 30
>>> L = 300
>>> g = pgauss(L, a*M/L)[0]
>>> gd = gabdual(g, a, M)
>>> # Plot in the time-domain
>>> _ = plt.plot(gd)
>>> plt.show()
.. image:: images/gabdual.png
:width: 700px
:alt: pgauss gabdual image
:align: center
.. seealso:: :func:`~ltfatpy.gabor.gabtight.gabtight`,
:func:`~ltfatpy.gabor.gabwin.gabwin`,
:func:`~ltfatpy.sigproc.fir2long.fir2long`,
:func:`~ltfatpy.gabor.dgt.dgt`
"""
# Verify a, M and L
if L is None:
if isinstance(g, np.ndarray):
Ls = g.shape[0]
else:
Ls = 1
L = dgtlength(Ls, a, M)
else:
Luser = dgtlength(L, a, M)
if L != Luser:
raise ValueError(("Incorrect transform length L={0:d} specified" +
" for a = {1:d} and M = {2:d}." +
" Next valid length is L={3:d}. See the help" +
" of DGTLENGTH for the requirements.").
format(L, a, M, Luser))
# Determine the window
(g, info) = _call_gabwin(g, a, M, L)
if L < info['gl']:
raise ValueError('Window is too long.')
R = 1
if (g.ndim > 1):
R = g.shape[1]
# Are we in the Riesz sequence of in the frame case
scale = 1
if a > M*R:
# Handle the Riesz basis (dual lattice) case.
# Swap a and M, and scale differently.
scale = a / M
a, M = M, a
# Compute
# Rectangular case
if info['gl'] <= M and R == 1:
# Diagonal of the frame operator
d = gabframediag(g, a, M, L)
gd = g / long2fir(g=d, L=info['gl'])
else:
# Long window case
# Just in case, otherwise the call is harmless.
g = fir2long(g, L)
gd = comp_gabdual_long(g, a, M)*scale
# post process result
if np.issubdtype(g.dtype, np.floating):
# If g is real then the output is known to be real.
gd = gd.real
return gd
def _call_gabwin(g, a, M, L):
from ltfatpy.gabor.gabwin import gabwin
return gabwin(g, a, M, L)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()