# -*- 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 dgt calculation
Ported from ltfat_2.1.0/gabor/dgt.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.comp.comp_sepdgt import comp_sepdgt
from ltfatpy.gabor.dgtlength import dgtlength
from ltfatpy.gabor.gabwin import gabwin
from ltfatpy.comp.assert_groworder import assert_groworder
from ltfatpy.comp.assert_sigreshape_pre import assert_sigreshape_pre
from ltfatpy.comp.assert_sigreshape_post import assert_sigreshape_post
[docs]def dgt(f, g, a, M, L=None, pt='freqinv'):
"""Discrete Gabor Transform
- Usage:
| ``(c, Ls, g) = dgt(f, g, a, M)``
| ``(c, Ls, g) = dgt(f, g, a, M, L)``
| ``(c, Ls, g) = dgt(f, g, a, M, L, pt)``
- Input parameters:
:param numpy.ndarray f: Input data. **f** dtype has to be float64 or
complex128.
:param g: Window function.
:param int a: Length of time shift.
:param int M: Number of channels.
:param int L: Length of transform to do. Default is None.
:param str pt: 'freqinv' or 'timeinv'. Default is 'freqinv'
:type g: str, dict or numpy.ndarray
- Output parameters:
:returns: ``(c, Ls, g)``
:rtype: tuple
:var numpy.ndarray c: :math:`M*N` array of gabor transform coefficients.
Its dtype is complex128.
:var int Ls: length of input signal
:var numpy.ndarray g: updated window function. Its dtype is float64 or
complex128 depending on **f** dtype.
``dgt(f, g, a, M)`` computes the Gabor coefficients (also known as a
windowed Fourier transform) of the input signal **f** with respect to the
window **g** and parameters **a** and **M**. The output is a one or two
dimensional :class:`numpy.ndarray` in a rectangular layout.
The length of the transform will be the smallest multiple of **a** and
**M** that is larger than the signal. **f** will be zero-extended to the
length of the transform. If **f** is a 2d array, the transformation is
applied to each column. The length of the transform done can be obtained
by ``L = c.shape[1] * a``
The window **g** may be an array of numerical values, a text string or a
dictionary. See the help of :func:`~ltfatpy.gabor.gabwin` for more
details.
``dgt(f, g, a, M, L)`` computes the Gabor coefficients as above, but does
a transform of length **L**. **f** will be cut or zero-extended to length
**L** before the transform is done.
``(c, Ls) = dgt(f, g, a, M)`` or ``(c, Ls) = dgt(f, g, a, M, L)`` returns
the length of the input signal **f**. This is handy for reconstruction:
- Examples:
In the following example we create a Hermite function, which is a
complex-valued function with a circular spectrogram, and visualize
the coefficients using both :func:`~matplotlib.pyplot.imshow` and
:func:`~ltfatpy.gabor.plotdgt.plotdgt`:
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from ltfatpy import plotdgt
>>> from ltfatpy import pherm
>>> a = 10
>>> M = 40
>>> L = a * M
>>> h, _ = pherm(L, 4) # 4th order hermite function.
>>> c = dgt(h, 'gauss', a, M)[0]
>>> # Simple plot: The squared modulus of the coefficients on
>>> # a linear scale
>>> _ = plt.imshow(np.abs(c)**2, interpolation='nearest', origin='upper')
>>> plt.show()
>>> # Better plot: zero-frequency is displayed in the middle,
>>> # and the coefficients are show on a logarithmic scale.
>>> _ = plotdgt(c, a, dynrange=50)
>>> plt.show()
.. image:: images/dgt_1.png
:width: 700px
:alt: imshow image
:align: center
.. image:: images/dgt_2.png
:width: 600px
:alt: plotdgt image
:align: center
``(c, Ls, g)=dgt(...)`` outputs the window used in the transform. This is
useful if the window was generated from a description in a string or
dictionary.
The Discrete Gabor Transform is defined as follows: Consider a window
**g** and a one-dimensional signal **f** of length **L** and define
:math:`N = L / a`. The output from ``c = dgt(f, g, a, M)`` is then given
by:
.. math::
c\\left(m+1,n+1\\right)=\\sum_{l=0}^{L-1}f(l+1)\\overline{g(l-an+1)}
e^{-2\\pi ilm/M}
where :math:`m=0,\ldots,M-1`, :math:`n=0,\ldots,N-1` and :math:`l-an`
are computed modulo **L**.
- Additional parameters:
``dgt`` takes the following keyword at the end of the line of input
arguments:
pt = 'freqinv'
Compute a DGT using a frequency-invariant phase. This
is the default convention described above.
pt = 'timeinv'
Compute a DGT using a time-invariant phase. This
convention is typically used in FIR-filter algorithms.
.. seealso:: :func:`~ltfatpy.gabor.idgt.idgt`,
:func:`~ltfatpy.gabor.gabwin.gabwin`, :func:`dwilt`,
:func:`~ltfatpy.gabor.gabdual.gabdual`,
:func:`~ltfatpy.gabor.phaselock.phaselock`
- References:
:cite:`fest98,gr01`
"""
# Verify f and determine its length
# Change f to correct shape.
(f, _unused, Ls, W, dim, permutedshape, order) = assert_sigreshape_pre(f,
L)
# Verify a, M and L
if L is None:
# Verify a, M and get L from the signal length f
L = dgtlength(Ls, a, M)
else:
# Verify a, M and get L
Luser = dgtlength(L, a, M)
if Luser != L:
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))
# verify pt
if pt == 'timeinv':
pt = 1
elif pt == 'freqinv':
pt = 0
else:
raise ValueError("pt argument should be 'timeinv' or 'freqinv'.")
# Determine the window
(gnum, info) = gabwin(g, a, M, L)
if L < info['gl']:
raise ValueError('Window is too long.')
# final cleanup
# Postpad
C = 0
if Ls < L:
f = np.concatenate((f, C*np.ones((L-Ls, W))), axis=0)
else:
f = f[:L]
# call the computation subroutines
c = comp_sepdgt(f, gnum, a, M, pt)
# flags_do_timeinv = 1
order = assert_groworder(order)
permutedshape = (M, L//a) + permutedshape[1:]
c = assert_sigreshape_post(c, dim, permutedshape, order)
if [i for i in c.shape if i > 2] and c.shape[0] == 1:
c = c.squeeze()
return (c, Ls, gnum)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()