1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
|
# -*- 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 S0 norm calculation
Ported from ltfat_2.1.0/gabor/s0norm.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
from numpy import linalg as LA
from ltfatpy.comp.assert_sigreshape_pre import assert_sigreshape_pre
from ltfatpy.comp.assert_sigreshape_post import assert_sigreshape_post
def s0norm(f, rel=False, dim=None):
"""S0-norm of signal
- Usage:
| ``y = s0norm(f)``
- Input parameters:
:param numpy.ndarray f: is the signal
:param bool rel: True if returning result should be relative to the
:math:`l^2` norm (the energy) of the signal.
False by default
:param int dim: dimension along which norm is applied (first
non-singleton dimension as default)
- Output parameters:
:return: s0-norm
:rtype: float
``s0norm(f)`` computes the :math:`S_0`-norm of a vector.
If the input is a matrix or ND-array, the :math:`S_0`-norm is computed
along the first (non-singleton) dimension, and a vector of values is
returned.
.. warning:: The :math:`S_0`-norm is computed by computing a full
short-time Fourier transform of a signal, which can be quite
time-consuming. Use this function with care for long signals.
"""
# ------ Computation --------------------------
(f, L, _unused, W, dim, permutedsize, order) = assert_sigreshape_pre(
f, dim=dim)
permutedsize_list = [1] + list(permutedsize[1:])
permutedsize = tuple(permutedsize_list)
if len(permutedsize_list) == 1:
permutedsize_list.append(1)
y = np.zeros(tuple(permutedsize_list), dtype=f.dtype)
g = __call_pgauss(L)
for ii in range(W):
# Compute the STFT by the simple algorithm and sum each column of the
# STFT as they are computed, to avoid L^2 memory usage.
for jj in range(L):
y[0, ii] = y[0, ii] + np.sum(np.abs(np.fft.fft(f[:, ii] *
np.roll(g, jj, axis=0))))
if rel:
y[0, ii] = y[0, ii] / LA.norm(f[:, ii])
y /= L
y = assert_sigreshape_post(y, dim, permutedsize, order)
return y
def __call_pgauss(L):
from ltfatpy.fourier.pgauss import pgauss
return pgauss(L)[0]
|
