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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 idgtreal calculation
Ported from ltfat_2.1.0/gabor/idgtreal.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.gabor.dgtlength import dgtlength
from ltfatpy.gabor.gabwin import gabwin
from ltfatpy.comp.comp_isepdgtreal import comp_isepdgtreal
from ltfatpy.tools.postpad import postpad
from ltfatpy.comp.comp_sigreshape_post import comp_sigreshape_post
def idgtreal(coef, g, a, M, Ls=None, pt='freqinv'):
"""Inverse discrete Gabor transform for real-valued signals
- Usage:
| ``(f, g) = idgtreal(c, g, a, M)``
| ``(f, g) = idgtreal(c, g, a, M, Ls)``
| ``(f, g) = idgtreal(c, g, a, M, Ls, pt)``
- Input parameters:
:param numpy.ndarray c: Array of coefficients
:param g: Window function
:param int a: Length of time shift
:param int M: Number of channels
:param int Ls: Length of signal
:param str pt: 'freqinv' or 'timeinv'. Default is 'freqinv'.
:type g: str, dict or numpy.ndarray
- Output parameters:
:returns: ``(f, g)``
:rtype: tuple
:var numpy.ndarray f: signal
:var numpy.ndarray g: window
``idgtreal(c, g, a, M)`` computes the Gabor expansion of the input
coefficients **c** with respect to the real-valued window **g**, time
shift **a** and number of channels **M**. **c** is assumed to be the
positive frequencies of the Gabor expansion of a real-valued signal.
It must hold that ``c.shape[0] == np.floor(M/2)+1``. Note that since the
correct number of channels cannot be deduced from the input, ``idgtreal``
takes an additional parameter as opposed to
:func:`~ltfatpy.gabor.idgt.idgt`.
The window **g** may be a vector of numerical values, a text string or a
dictionary. See the help of :func:`~ltfatpy.gabor.gabwin.gabwin` for more
details.
``idgtreal(c, g, a, M, Ls)`` does as above but cuts or extends **f** to
length **Ls**.
``(f, g) = idgtreal(...)`` outputs the window used in the transform. This
is useful if the window was generated from a description in a string or
dictionary.
For perfect reconstruction, the window used must be a dual window of the
one used to generate the coefficients.
If **g** is a row vector, then the output will also be a row vector. If
**c** is 3-dimensional, then ``idgtreal`` will return a matrix consisting
of one column vector for each of the TF-planes in **c**.
See the help on :func:`~ltfatpy.gabor.idgt.idgt` for the precise definition
of the inverse Gabor transform.
- Additional parameters
``idgtreal`` optionnaly takes a **pt** arguments that can take the
following values:
========== ===========================================================
'freqinv' Compute a ``idgtreal`` using a frequency-invariant phase.
This is the default convention described in the help for
:func:`~ltfatpy.gabor.dgt.dgt`.
'timeinv' Compute a ``idgtreal`` using a time-invariant phase. This
convention is typically used in filter bank algorithms.
========== ===========================================================
- Examples
The following example demonstrates the basic principles for getting
perfect reconstruction (short version)::
>>> from ltfatpy import greasy
>>> from ltfatpy import dgtreal
>>> f = greasy()[0] # Input test signal
>>> a = 32 # time shift
>>> M = 64 # frequency shift
>>> gs = {'name': 'blackman', 'M': 128} # synthesis window
>>> # analysis window
>>> ga = {'name' : ('dual', gs['name']), 'M' : gs['M']}
>>> (c, Ls) = dgtreal(f, ga, a, M)[0:2] # analysis
>>> r = idgtreal(c, gs, a, M, Ls)[0] # synthesis
>>> np.linalg.norm(f-r) < 1e-10 # test
True
.. seealso:: :func:`~ltfatpy.gabor.idgt.idgt`,
:func:`~ltfatpy.gabor.gabwin.gabwin`,
:func:`~ltfatpy.gabor.gabdual.gabdual`, :func:`dwilt`
"""
if (not isinstance(g, np.ndarray) and not isinstance(g, str) and
not isinstance(g, dict)):
raise TypeError('g must be a numpy.array or str or dict.')
if (isinstance(g, np.ndarray) and g.size < 2):
raise ValueError('g must be a vector (you probably forgot to supply' +
' the window function as input parameter.)')
# Define initial value for flags and key/value pairs.
if coef.ndim < 2:
raise ValueError('coef must have at least 2 dimensions')
N = coef.shape[1]
if coef.ndim > 2:
W = coef.shape[2]
else:
W = 1
# Make a dummy call to test the input parameters
Lsmallest = dgtlength(1, a, M)
M2 = np.floor(M/2)+1
if M2 != coef.shape[0]:
mess = ('Mismatch between the specified number of channels ' +
'and the size of the input coefficients: ' +
'M2 = {0:f}, coef.shape = {1:s}')
raise ValueError(mess.format(M2, '%s' % (coef.shape, )))
L = N * a
if L % Lsmallest > 0:
raise ValueError('Invalid size of coefficient array.')
# Determine the window
(g, info) = gabwin(g, a, M, L)
if L < info['gl']:
raise ValueError('Window is too long.')
if not np.issubdtype(g.dtype, np.floating):
raise ValueError('The window must be real-valued.')
# verify pt
if pt == 'timeinv':
pt = 1
elif pt == 'freqinv':
pt = 0
else:
mes = "pt (" + str(pt) + ") argument should be 'timeinv' or 'freqinv'."
raise ValueError(mes)
# Do the actual computation.
f = comp_isepdgtreal(coef, g, a, M, pt)
# Cut or extend f to the correct length, if desired.
if Ls is not None:
f = postpad(f, Ls)
else:
Ls = L
f = comp_sigreshape_post(f, Ls, 0, (0, W))
return (f, g)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()
|
