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# -*- coding: utf-8 -*-
# ######### COPYRIGHT #########
# Credits
# #######
#
# Copyright(c) 2015-2025
# ----------------------
#
# * `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) 2005-2025 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 = 1.1.2
# * 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 tight windows calculation
Ported from ltfat_2.1.0/gabor/gabtight.m
.. moduleauthor:: Denis Arrivault,
Florent Jaillet
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.gabor.dgtlength import dgtlength
from ltfatpy.sigproc.fir2long import fir2long
from ltfatpy.sigproc.long2fir import long2fir
from ltfatpy.gabor.gabframediag import gabframediag
from ltfatpy.comp.comp_gabtight_long import comp_gabtight_long
def gabtight(g, a, M, L=None):
"""Canonical tight window of Gabor frame
- Usage:
| ``gt = gabtight(None, a, M, L)``
| ``gt = gabtight(g, a, M)``
| ``gt = gabtight(g, a, M, L)``
- Input parameters:
:param g: Gabor window
:type g: numpy.ndarray or str or dict
:param int a: Length of time shift
:param int M: Number of modulations
:param int L: Length of window (optional except if **g** is None)
- Output parameters:
:return: Canonical tight window
:rtype: numpy.ndarray
``gabtight(None, a, M, L)`` computes a nice tight window of length **L**
for a lattice with parameters **a**, **M**. The window is not an FIR
window, meaning that it will only generate a tight system if the system
length is equal to **L**.
``gabtight(g, a, M)`` computes the canonical tight window of the 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. See the help of :func:`~ltfatpy.gabor.gabwin` for more details.
If the length of **g** is equal to **M**, then the input window is assumed
to be a 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.
``gabtight(g, a, M, L)`` returns a window that is tight for a system of
length **L**. Unless the input window **g** is a FIR window, the returned
tight window will have length **L**.
If ``a > M`` then an orthonormal window of the Gabor Riesz sequence
with window **g** and parameters **a** and **M** will be calculated.
- Examples:
The following example shows the canonical tight window of the Gaussian
window. This is calculated by default by
:func:`~ltfatpy.gabor.gabtight` if no window is specified:
>>> import matplotlib.pyplot as plt
>>> from ltfatpy import gabtight
>>> a = 20
>>> M = 30
>>> L = 300
>>> gt = gabtight(None, a, M, L)
>>> # Plot in the time-domain
>>> _ = plt.plot(gt)
>>> plt.show()
.. image:: images/gabtight.png
:width: 700px
:alt: pgauss gabtight image
:align: center
.. seealso:: :func:`~ltfatpy.gabor.gabdual.gabdual`,
:func:`~ltfatpy.gabor.gabwin.gabwin`,
:func:`~ltfatpy.sigproc.fir2long.fir2long`,
:func:`~ltfatpy.gabor.dgt.dgt`
"""
# Verify a, M and L
if g is None:
g = 'gauss'
if L is None:
if not isinstance(g, np.ndarray):
Ls = 1
else:
Ls = g.shape[0]
L = dgtlength(Ls, a, M)
else:
Luser = dgtlength(L, a, M)
if L != Luser:
raise ValueError(("Incorrect transform length L={0:d} specified." +
" Next valid length is L={1:d}. See the help" +
" of DGTLENGTH for the requirements.").format(L,
Luser))
# Determine the window
(g, info) = _call_gabwin(g, a, M, L)
if L < info['gl']:
raise ValueError('Window is too long.\n')
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 = np.sqrt(a/M)
a, M = M, a
# Compute the rectangular case
if info['gl'] <= M and R == 1:
# Diagonal of the frame operator
d = gabframediag(g, a, M, L)
gt = g / np.sqrt(long2fir(d, info['gl']))
else:
# Long window case
# Just in case, otherwise the call is harmless.
g = fir2long(g, L)
gt = comp_gabtight_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.
gt = gt.real
return gt
def _call_gabwin(g, a, M, L):
# gabwin is imported in a different function to avoid circular imports
from ltfatpy.gabor.gabwin import gabwin
return gabwin(g, a, M, L)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()
|
