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