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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 DSTI function
Ported from ltfat_2.1.0/fourier/dsti.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
from ltfatpy.comp.comp_dst import comp_dst
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 dsti(f, L=None, dim=None):
r"""Discrete Sine Transform type I
- Usage:
| ``c = dsti(f)``
| ``c = dsti(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
``dsti(f)`` computes the discrete sine transform of type I of the
input signal **f**. If **f** is multi-dimensional, the transformation is
applied along the first non-singleton dimension.
``dsti(f,L)`` zero-pads or truncates **f** to length **L** before doing the
transformation.
``dsti(f,[],dim)`` or ``dsti(f,L,dim)`` applies the transformation along
dimension **dim**.
The transform is real (output is real if input is real) and orthonormal.
This transform is its own inverse.
Let f be a signal of length **L** and let ``c=dsti(f)``. Then
.. math::
c\\left(n+1\\right)=\\sqrt{\\frac{2}{L+1}}\\sum_{m=0}^{L-1}f\\left(
m+1\\right)\\sin\\left(\\frac{\\pi \\left(n+1\\right)\\left(
m+1\\right)}{L+1}\\right)
The implementation of this functions uses a simple algorithm that requires
an FFT of length $2N+2$, which might potentially be the product of a large
prime number. This may cause the function to sometimes execute slowly.
If guaranteed high speed is a concern, please consider using one of the
other DST transforms.
- Examples:
The following figures show the first 4 basis functions of the DSTI of
length 20:
>>> import numpy as np
>>> # The dsti is its own adjoint.
>>> F = dsti(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/dsti.png
:width: 700px
:alt: dsti image
:align: center
.. seealso:: :func:`~ltfatpy.fourier.dstii`,
:func:`~ltfatpy.fourier.dstiii`, :func:`~ltfatpy.fourier.dstiv`,
:func:`~ltfatpy.fourier.dcti`
- 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_dst(f, 1)
return assert_sigreshape_post(c, dim, permutedsize, order)
if __name__ == '__main__': # pragma: no cover
import doctest
doctest.testmod()
|
