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Module « numpy.matlib »

Fonction hamming - module numpy.matlib

Signature de la fonction hamming

def hamming(M) 

Description

help(numpy.matlib.hamming)

Return the Hamming window.

The Hamming 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
    The window, with the maximum value normalized to one (the value
    one appears only if the number of samples is odd).

See Also
--------
bartlett, blackman, hanning, kaiser

Notes
-----
The Hamming window is defined as

.. math::  w(n) = 0.54 - 0.46\cos\left(\frac{2\pi{n}}{M-1}\right)
           \qquad 0 \leq n \leq M-1

The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
and is described in Blackman and Tukey. It was recommended for
smoothing the truncated autocovariance function in the time domain.
Most references to the Hamming 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. 109-110.
.. [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.hamming(12)
array([ 0.08      ,  0.15302337,  0.34890909,  0.60546483,  0.84123594, # may vary
        0.98136677,  0.98136677,  0.84123594,  0.60546483,  0.34890909,
        0.15302337,  0.08      ])

Plot the window and the frequency response.

.. plot::
    :include-source:

    import matplotlib.pyplot as plt
    from numpy.fft import fft, fftshift
    window = np.hamming(51)
    plt.plot(window)
    plt.title("Hamming 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))
    response = 20 * np.log10(mag)
    response = np.clip(response, -100, 100)
    plt.plot(freq, response)
    plt.title("Frequency response of Hamming window")
    plt.ylabel("Magnitude [dB]")
    plt.xlabel("Normalized frequency [cycles per sample]")
    plt.axis('tight')
    plt.show()

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