Vous êtes un professionnel et vous avez besoin d'une formation ? Deep Learning avec Python
et Keras et Tensorflow Voir le programme détaillé

Module « numpy »

Fonction bartlett - module numpy

Signature de la fonction bartlett

def bartlett(M) 

Description

help(numpy.bartlett)

Return the Bartlett window.

The Bartlett window is very similar to a triangular window, except
that the end points are at zero.  It is often used in signal
processing for tapering a signal, without generating too much
ripple in the frequency domain.

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

Returns
-------
out : array
    The triangular window, with the maximum value normalized to one
    (the value one appears only if the number of samples is odd), with
    the first and last samples equal to zero.

See Also
--------
blackman, hamming, hanning, kaiser

Notes
-----
The Bartlett window is defined as

.. math:: w(n) = \frac{2}{M-1} \left(
          \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right|
          \right)

Most references to the Bartlett window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values.  Note that convolution with this window produces linear
interpolation.  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. The Fourier transform of the
Bartlett window is the product of two sinc functions. Note the excellent
discussion in Kanasewich [2]_.

References
----------
.. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra",
       Biometrika 37, 1-16, 1950.
.. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
       The University of Alberta Press, 1975, pp. 109-110.
.. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal
       Processing", Prentice-Hall, 1999, pp. 468-471.
.. [4] Wikipedia, "Window function",
       https://en.wikipedia.org/wiki/Window_function
.. [5] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
       "Numerical Recipes", Cambridge University Press, 1986, page 429.

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> np.bartlett(12)
array([ 0.        ,  0.18181818,  0.36363636,  0.54545455,  0.72727273, # may vary
        0.90909091,  0.90909091,  0.72727273,  0.54545455,  0.36363636,
        0.18181818,  0.        ])

Plot the window and its frequency response (requires SciPy and matplotlib).

.. plot::
    :include-source:

    import matplotlib.pyplot as plt
    from numpy.fft import fft, fftshift
    window = np.bartlett(51)
    plt.plot(window)
    plt.title("Bartlett 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 Bartlett window")
    plt.ylabel("Magnitude [dB]")
    plt.xlabel("Normalized frequency [cycles per sample]")
    plt.axis('tight')
    plt.show()

Vous êtes un professionnel et vous avez besoin d'une formation ? Machine Learning
avec Scikit-Learn Voir le programme détaillé