Module « scipy.signal »

Fonction hamming - module scipy.signal

Signature de la fonction hamming

def hamming(*args, **kwargs) 

Description

hamming.__doc__

Return a Hamming window.

    The Hamming window is a taper formed by using a raised cosine with
    non-zero endpoints, optimized to minimize the nearest side lobe.

    .. warning:: scipy.signal.hamming is deprecated,
                 use scipy.signal.windows.hamming instead.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an empty
        array is returned.
    sym : bool, optional
        When True (default), generates a symmetric window, for use in filter
        design.
        When False, generates a periodic window, for use in spectral analysis.

    Returns
    -------
    w : ndarray
        The window, with the maximum value normalized to 1 (though the value 1
        does not appear if `M` is even and `sym` is True).

    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
    --------
    Plot the window and its frequency response:

    >>> from scipy import signal
    >>> from scipy.fft import fft, fftshift
    >>> import matplotlib.pyplot as plt

    >>> window = signal.windows.hamming(51)
    >>> plt.plot(window)
    >>> plt.title("Hamming window")
    >>> plt.ylabel("Amplitude")
    >>> plt.xlabel("Sample")

    >>> plt.figure()
    >>> A = fft(window, 2048) / (len(window)/2.0)
    >>> freq = np.linspace(-0.5, 0.5, len(A))
    >>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
    >>> plt.plot(freq, response)
    >>> plt.axis([-0.5, 0.5, -120, 0])
    >>> plt.title("Frequency response of the Hamming window")
    >>> plt.ylabel("Normalized magnitude [dB]")
    >>> plt.xlabel("Normalized frequency [cycles per sample]")