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Module « scipy.linalg »

Fonction dft - module scipy.linalg

Signature de la fonction dft

def dft(n, scale=None) 

Description

help(scipy.linalg.dft)

Discrete Fourier transform matrix.

Create the matrix that computes the discrete Fourier transform of a
sequence [1]_. The nth primitive root of unity used to generate the
matrix is exp(-2*pi*i/n), where i = sqrt(-1).

Parameters
----------
n : int
    Size the matrix to create.
scale : str, optional
    Must be None, 'sqrtn', or 'n'.
    If `scale` is 'sqrtn', the matrix is divided by `sqrt(n)`.
    If `scale` is 'n', the matrix is divided by `n`.
    If `scale` is None (the default), the matrix is not normalized, and the
    return value is simply the Vandermonde matrix of the roots of unity.

Returns
-------
m : (n, n) ndarray
    The DFT matrix.

Notes
-----
When `scale` is None, multiplying a vector by the matrix returned by
`dft` is mathematically equivalent to (but much less efficient than)
the calculation performed by `scipy.fft.fft`.

.. versionadded:: 0.14.0

References
----------
.. [1] "DFT matrix", https://en.wikipedia.org/wiki/DFT_matrix

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import dft
>>> np.set_printoptions(precision=2, suppress=True)  # for compact output
>>> m = dft(5)
>>> m
array([[ 1.  +0.j  ,  1.  +0.j  ,  1.  +0.j  ,  1.  +0.j  ,  1.  +0.j  ],
       [ 1.  +0.j  ,  0.31-0.95j, -0.81-0.59j, -0.81+0.59j,  0.31+0.95j],
       [ 1.  +0.j  , -0.81-0.59j,  0.31+0.95j,  0.31-0.95j, -0.81+0.59j],
       [ 1.  +0.j  , -0.81+0.59j,  0.31-0.95j,  0.31+0.95j, -0.81-0.59j],
       [ 1.  +0.j  ,  0.31+0.95j, -0.81+0.59j, -0.81-0.59j,  0.31-0.95j]])
>>> x = np.array([1, 2, 3, 0, 3])
>>> m @ x  # Compute the DFT of x
array([ 9.  +0.j  ,  0.12-0.81j, -2.12+3.44j, -2.12-3.44j,  0.12+0.81j])

Verify that ``m @ x`` is the same as ``fft(x)``.

>>> from scipy.fft import fft
>>> fft(x)     # Same result as m @ x
array([ 9.  +0.j  ,  0.12-0.81j, -2.12+3.44j, -2.12-3.44j,  0.12+0.81j])

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