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Module « numpy.matlib »

Fonction hanning - module numpy.matlib

Signature de la fonction hanning

def hanning(M) 

Description

help(numpy.matlib.hanning)

Return the Hanning window.

The Hanning window is a taper formed by using a weighted cosine.

Parameters
----------
M : int
    Number of points in the output window. If zero or less, an
    empty array is returned.

Returns
-------
out : ndarray, shape(M,)
    The window, with the maximum value normalized to one (the value
    one appears only if `M` is odd).

See Also
--------
bartlett, blackman, hamming, kaiser

Notes
-----
The Hanning window is defined as

.. math::  w(n) = 0.5 - 0.5\cos\left(\frac{2\pi{n}}{M-1}\right)
           \qquad 0 \leq n \leq M-1

The Hanning was named for Julius von Hann, an Austrian meteorologist.
It is also known as the Cosine Bell. Some authors prefer that it be
called a Hann window, to help avoid confusion with the very similar
Hamming window.

Most references to the Hanning window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values.  It is also known as an apodization (which means
"removing the foot", i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.

References
----------
.. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
       spectra, Dover Publications, New York.
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
       The University of Alberta Press, 1975, pp. 106-108.
.. [3] Wikipedia, "Window function",
       https://en.wikipedia.org/wiki/Window_function
.. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
       "Numerical Recipes", Cambridge University Press, 1986, page 425.

Examples
--------
>>> import numpy as np
>>> np.hanning(12)
array([0.        , 0.07937323, 0.29229249, 0.57115742, 0.82743037,
       0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,
       0.07937323, 0.        ])

Plot the window and its frequency response.

.. plot::
    :include-source:

    import matplotlib.pyplot as plt
    from numpy.fft import fft, fftshift
    window = np.hanning(51)
    plt.plot(window)
    plt.title("Hann window")
    plt.ylabel("Amplitude")
    plt.xlabel("Sample")
    plt.show()

    plt.figure()
    A = fft(window, 2048) / 25.5
    mag = np.abs(fftshift(A))
    freq = np.linspace(-0.5, 0.5, len(A))
    with np.errstate(divide='ignore', invalid='ignore'):
        response = 20 * np.log10(mag)
    response = np.clip(response, -100, 100)
    plt.plot(freq, response)
    plt.title("Frequency response of the Hann window")
    plt.ylabel("Magnitude [dB]")
    plt.xlabel("Normalized frequency [cycles per sample]")
    plt.axis('tight')
    plt.show()

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