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Module « scipy.special »

Fonction sinc - module scipy.special

Signature de la fonction sinc

def sinc(x) 

Description

help(scipy.special.sinc)

Return the normalized sinc function.

The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
:math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
only everywhere continuous but also infinitely differentiable.

.. note::

    Note the normalization factor of ``pi`` used in the definition.
    This is the most commonly used definition in signal processing.
    Use ``sinc(x / np.pi)`` to obtain the unnormalized sinc function
    :math:`\sin(x)/x` that is more common in mathematics.

Parameters
----------
x : ndarray
    Array (possibly multi-dimensional) of values for which to calculate
    ``sinc(x)``.

Returns
-------
out : ndarray
    ``sinc(x)``, which has the same shape as the input.

Notes
-----
The name sinc is short for "sine cardinal" or "sinus cardinalis".

The sinc function is used in various signal processing applications,
including in anti-aliasing, in the construction of a Lanczos resampling
filter, and in interpolation.

For bandlimited interpolation of discrete-time signals, the ideal
interpolation kernel is proportional to the sinc function.

References
----------
.. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
       Resource. https://mathworld.wolfram.com/SincFunction.html
.. [2] Wikipedia, "Sinc function",
       https://en.wikipedia.org/wiki/Sinc_function

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-4, 4, 41)
>>> np.sinc(x)
 array([-3.89804309e-17,  -4.92362781e-02,  -8.40918587e-02, # may vary
        -8.90384387e-02,  -5.84680802e-02,   3.89804309e-17,
        6.68206631e-02,   1.16434881e-01,   1.26137788e-01,
        8.50444803e-02,  -3.89804309e-17,  -1.03943254e-01,
        -1.89206682e-01,  -2.16236208e-01,  -1.55914881e-01,
        3.89804309e-17,   2.33872321e-01,   5.04551152e-01,
        7.56826729e-01,   9.35489284e-01,   1.00000000e+00,
        9.35489284e-01,   7.56826729e-01,   5.04551152e-01,
        2.33872321e-01,   3.89804309e-17,  -1.55914881e-01,
       -2.16236208e-01,  -1.89206682e-01,  -1.03943254e-01,
       -3.89804309e-17,   8.50444803e-02,   1.26137788e-01,
        1.16434881e-01,   6.68206631e-02,   3.89804309e-17,
        -5.84680802e-02,  -8.90384387e-02,  -8.40918587e-02,
        -4.92362781e-02,  -3.89804309e-17])

>>> plt.plot(x, np.sinc(x))
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Sinc Function")
Text(0.5, 1.0, 'Sinc Function')
>>> plt.ylabel("Amplitude")
Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("X")
Text(0.5, 0, 'X')
>>> plt.show()

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