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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 #########
"""This module contains sampled, periodized Gaussian window function
Ported from ltfat_2.1.0/fourier/pgauss.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
from ltfatpy.comp import comp_pgauss as pg
from ltfatpy.sigproc.normalize import normalize
def pgauss(L, tfr=1.0, fs=0.0, width=0.0, bw=0.0, c_f=0.0, centering='wp',
delay=0.0, norm='2', **kwargs):
"""Sampled, periodized Gaussian
- Usage:
| ``(g, tfr) = pgauss(L)``
| ``(g, tfr) = pgauss(L, tfr, fs, width, bw, c_f, centering, delay,
norm)``
- Input parameters:
:param int L: Length of the output vector.
:param float tfr: determines the ratio between the effective support
of **g** and the effective support of the DFT of **g**. If
:math:`tfr>1` then **g** has a wider support than the DFT of **g**.
Default is 1.
:param float fs: Use a sampling rate of **fs** Hz as unit for specifying
the width, bandwidth, centre frequency and delay of the Gaussian.
Default is :math:`fs=0` which indicates to measure everything in
samples.
:param float width: Set the width of the Gaussian such that it has an
effective support of **width** samples. This means that
approx. 96% of the energy or 79% of the area under the graph is
contained within **width** samples. This corresponds to a -6 db
cutoff. This is equivalent to calling ``pgauss(L,tfr = s^2/L)``.
Default is zero, unset.
:param float bw: As for the **width** argument, but specifies the width
in the frequency domain. The bandwidth is measured in normalized
frequencies, unless the **fs** value is given. Default is zero, unset.
:param float c_f: Set the centre frequency of the Gaussian to **cf**.
Default is zero.
:param str centering: "wp" means output is whole point even. This is the
default. Setting it to **hp** means output is half point even which
is the case for the most Matlab filters routines.
:param float delay: Delay the output by **delay**. Default is zero.
:param str norm: normalization to apply (default is L2)
- Normalization types :
+-------+---------+
| Name | Norms |
+=======+=========+
| '1' | L1-norm |
+-------+---------+
| '2' | L2-norm |
+-------+---------+
- Output parameters:
:returns: ``(g, tfr)``
:rtype: tuple
:var numpy array g: window array of length **L**
:var int tfr: ratio between the effective support of **g** and the
effective support of the DFT of **g**.
``pgauss(L,tfr)`` samples of a periodized Gaussian. The function returns
a numpy array **g** containing a regular sampling of the periodization of
the function :math:`\\exp(-\\pi*(x^2/tfr))`.
The :math:`l^2` norm of the returned Gaussian is equal to 1.
The function is whole-point even. This implies that
``fft(pgauss(L, tfr))`` is real for any **L** and **tfr**. The DFT of
**g** is equal to ``pgauss(L, 1/tfr)``.
If this function is used to generate a window for a Gabor frame, then
the window giving the smallest frame bound ratio is generated by
``pgauss(L, a*M/L)``.
- Examples:
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from ltfatpy import sgram
>>> # This example creates a Gaussian function, and demonstrates that it is
>>> # its own Discrete Fourier Transform:
>>> g = pgauss(128)[0]
>>> # Test of DFT invariance: Should be close to zero.
>>> np.linalg.norm(g - np.fft.fft(g)/np.sqrt(128)) <= 1e-10
True
>>> # The next plot shows the Gaussian in the time domain:
>>> _ = plt.plot(np.fft.fftshift(g))
>>> plt.show()
>>> # The next plot shows the Gaussian in the time-frequency plane:
>>> _ = sgram(g, nf=True, tc=True, normalization='lin')
>>> plt.show()
.. image:: images/pgauss_1.png
:width: 700px
:alt: Gaussian in the time domain
:align: center
.. image:: images/pgauss_2.png
:width: 700px
:alt: Gaussian in the time-frequency plane
:align: center
.. note:: **g** is real if **c_f** = 0 and complex if not.
.. seealso:: :func:`~ltfatpy.gabor.dgtlength.dgtlength`,
:func:`~ltfatpy.fourier.psech.psech`,
:func:`~ltfatpy.sigproc.firwin.firwin`, :func:`pbspline`,
:func:`~ltfatpy.sigproc.normalize.normalize`
"""
cent = 0
if centering == 'hp':
cent = 0.5
elif centering != 'wp':
raise ValueError("centering should be 'wp' or 'hp'")
if (type(L) is not int or L <= 0):
raise TypeError("L should be non null integer")
if(type(tfr) is int):
tfr = float(tfr)
if (type(tfr) is not float):
raise TypeError("tfr should be float")
if fs == 0:
if width != 0:
tfr = width**2 / L
if bw != 0:
tfr = L / (bw * L/2)**2
else:
if width != 0:
tfr = (width * fs)**2 / L
if bw != 0:
tfr = L / (bw / fs * L)**2
delay = delay*fs
c_f = c_f/fs*L
g = pg.comp_pgauss(L, tfr, cent-delay, c_f)
g = normalize(g, norm)[0]
return(g, tfr)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()
|
