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
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
# -*- 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 DCTII function
Ported from ltfat_2.1.0/fourier/dctii.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.comp.comp_dct import comp_dct
from ltfatpy.comp.assert_sigreshape_pre import assert_sigreshape_pre
from ltfatpy.comp.assert_sigreshape_post import assert_sigreshape_post
from ltfatpy.tools.postpad import postpad
def dctii(f, L=None, dim=None):
r"""Discrete Cosine Transform type II
- Usage:
| ``c = dctii(f)``
| ``c = dctii(f,L,dim)``
- Input parameters:
:param numpy.ndarray f: Input data. **f** dtype has to be float64 or
complex128.
:param int L: Length of the output vector. Default is the length of
**f**.
:param int dim: dimension along which the transformation is applied.
Default is the first non-singleton dimension.
- Output parameter:
:return: ``c``
:rtype: numpy.ndarray
``dctii(f)`` computes the discrete cosine transform of type II of the
input signal **f**. If **f** is a matrix then the transformation is applied
to each column. For N-D arrays, the transformation is applied to the first
non-singleton dimension.
``dctii(f,L)`` zero-pads or truncates **f** to length **L** before doing
the transformation.
``dctii(f,dim=dim)`` or ``dctii(f,L,dim)`` applies the transformation along
dimension **dim**.
The transform is real (output is real if input is real) and
it is orthonormal.
This is the inverse of \\|dctiii\\|.
Let f be a signal of length **L**, let :math:`c=dctii(f)` and define the
vector **w** of length **L** by
.. w = [1/sqrt(2) 1 1 1 1 ...]
.. math::
w\\left(n\\right)=\\begin{cases}\\frac{1}{\\sqrt{2}} & \\text{if }n=0
\\ 1 & \\text{otherwise}\\end{cases}
Then
.. math::
c\\left(n+1\\right)=\\sqrt{\\frac{2}{L}}\\sum_{m=0}^{L-1}w\\left(
n\\right)f\\left(m+1\\right)\\cos\\left(\\frac{\\pi}{L} n\\left(
m+\\frac{1}{2}\\right)\\right)
- Examples:
The following figures show the first 4 basis functions of the DCTII of
length 20:
>>> import numpy as np
>>> # The dctii is its own adjoint.
>>> F = dctii(np.eye(20, dtype=np.float64))
>>> import matplotlib.pyplot as plt
>>> plt.close('all')
>>> fig = plt.figure()
>>> for ii in range(1,5):
... ax = fig.add_subplot(4,1,ii)
... ax.stem(F[:,ii-1])
...
<Container object of 3 artists>
<Container object of 3 artists>
<Container object of 3 artists>
<Container object of 3 artists>
>>> plt.show()
.. image:: images/dctii.png
:width: 700px
:alt: dctii image
:align: center
.. seealso:: :func:`~ltfatpy.fourier.dctiii`,
:func:`~ltfatpy.fourier.dctiv`, :func:`~ltfatpy.fourier.dstii`
- References:
:cite:`rayi90,wi94`
"""
(f, L, _, _, dim, permutedsize, order) = assert_sigreshape_pre(f, L, dim)
if L is not None:
f = postpad(f, L)
if L == 1:
c = f
else:
c = comp_dct(f, 2)
if f.dtype.type == np.float64:
c = np.real(c)
return assert_sigreshape_post(c, dim, permutedsize, order)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()
|
