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Module « numpy.matlib »

Fonction blackman - module numpy.matlib

Signature de la fonction blackman

def blackman(M) 

Description

help(numpy.matlib.blackman)

Return the Blackman window.

The Blackman window is a taper formed by using the first three
terms of a summation of cosines. It was designed to have close to the
minimal leakage possible.  It is close to optimal, only slightly worse
than a Kaiser window.

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, hamming, hanning, kaiser

Notes
-----
The Blackman window is defined as

.. math::  w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)

Most references to the Blackman 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. It is known as a
"near optimal" tapering function, almost as good (by some measures)
as the kaiser window.

References
----------
Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
Dover Publications, New York.

Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> np.blackman(12)
array([-1.38777878e-17,   3.26064346e-02,   1.59903635e-01, # may vary
        4.14397981e-01,   7.36045180e-01,   9.67046769e-01,
        9.67046769e-01,   7.36045180e-01,   4.14397981e-01,
        1.59903635e-01,   3.26064346e-02,  -1.38777878e-17])

Plot the window and the frequency response.

.. plot::
    :include-source:

    import matplotlib.pyplot as plt
    from numpy.fft import fft, fftshift
    window = np.blackman(51)
    plt.plot(window)
    plt.title("Blackman window")
    plt.ylabel("Amplitude")
    plt.xlabel("Sample")
    plt.show()  # doctest: +SKIP

    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 Blackman window")
    plt.ylabel("Magnitude [dB]")
    plt.xlabel("Normalized frequency [cycles per sample]")
    plt.axis('tight')
    plt.show()

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