Module « scipy.signal »

Fonction chebwin - module scipy.signal

Signature de la fonction chebwin

def chebwin(*args, **kwargs) 

Description

chebwin.__doc__

Return a Dolph-Chebyshev window.

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

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an empty
        array is returned.
    at : float
        Attenuation (in dB).
    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 always normalized to 1

    Notes
    -----
    This window optimizes for the narrowest main lobe width for a given order
    `M` and sidelobe equiripple attenuation `at`, using Chebyshev
    polynomials.  It was originally developed by Dolph to optimize the
    directionality of radio antenna arrays.

    Unlike most windows, the Dolph-Chebyshev is defined in terms of its
    frequency response:

    .. math:: W(k) = \frac
              {\cos\{M \cos^{-1}[\beta \cos(\frac{\pi k}{M})]\}}
              {\cosh[M \cosh^{-1}(\beta)]}

    where

    .. math:: \beta = \cosh \left [\frac{1}{M}
              \cosh^{-1}(10^\frac{A}{20}) \right ]

    and 0 <= abs(k) <= M-1. A is the attenuation in decibels (`at`).

    The time domain window is then generated using the IFFT, so
    power-of-two `M` are the fastest to generate, and prime number `M` are
    the slowest.

    The equiripple condition in the frequency domain creates impulses in the
    time domain, which appear at the ends of the window.

    References
    ----------
    .. [1] C. Dolph, "A current distribution for broadside arrays which
           optimizes the relationship between beam width and side-lobe level",
           Proceedings of the IEEE, Vol. 34, Issue 6
    .. [2] Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal Filter",
           American Meteorological Society (April 1997)
           http://mathsci.ucd.ie/~plynch/Publications/Dolph.pdf
    .. [3] F. J. Harris, "On the use of windows for harmonic analysis with the
           discrete Fourier transforms", Proceedings of the IEEE, Vol. 66,
           No. 1, January 1978

    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.chebwin(51, at=100)
    >>> plt.plot(window)
    >>> plt.title("Dolph-Chebyshev window (100 dB)")
    >>> 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 Dolph-Chebyshev window (100 dB)")
    >>> plt.ylabel("Normalized magnitude [dB]")
    >>> plt.xlabel("Normalized frequency [cycles per sample]")