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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 #########
"""Module of inverse normalized discrete Fourier transform
Ported from ltfat_2.1.0/fourier/idft.m
.. moduleauthor:: Florent Jaillet
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.comp.assert_sigreshape_pre import assert_sigreshape_pre
from ltfatpy.comp.assert_sigreshape_post import assert_sigreshape_post
def idft(c, N=None, dim=0):
r"""Inverse Normalized Discrete Fourier Transform
- Usage:
| ``f = idft(c)``
| ``f = idft(c, N, dim)``
- Input parameters:
:param numpy.ndarray c: Normalized discrete Fourier coefficients of a
signal
:param int N: IDFT length
:param int dim: Axis over which to compute the IDFT. By default the first
axis is used.
- Output parameters:
:returns: Reconstructed signal
:rtype: numpy.ndarray
:func:`~ltfatpy.fourier.idft.idft` computes a normalized or unitary inverse
discrete Fourier transform.
The unitary inverse discrete Fourier transform is computed by
.. L-1
f(l+1) = 1/sqrt(L) * sum c(k+1)*exp(2*pi*i*k*l/L)
k=0
.. math::
f\\left(l+1\\right)=\\frac{1}{\\sqrt{L}}
\\sum_{k=0}^{L-1}c\\left(k+1\\right)e^{2\\pi ikl/L}
for :math:`l=0, \\ldots, L-1`.
The output of :func:`~ltfatpy.fourier.idft.idft` is a scaled version of the
output from :func:`numpy.fft.ifft`. The function takes the same first three
arguments as :func:`numpy.fft.ifft`. See the help on :func:`numpy.fft.ifft`
for a thorough description.
.. seealso:: :func:`~ltfatpy.fourier.dft.dft`
"""
c, N, Ls, W, dim, permutedsize, order = assert_sigreshape_pre(c, N, dim)
# Force ifft along dimension 0, since we have permuted the dimensions
# manually
f = np.fft.ifft(c, N, 0) * np.sqrt(N)
f = assert_sigreshape_post(f, dim, permutedsize, order)
return f
|
