Function blackman_harris

numpy_ml/utils/windows.py:4–40

The Blackman-Harris window. Notes ----- The Blackman-Harris window is an instance of the more general class of cosine-sum windows where `K=3`. Additional coefficients extend the Hamming window to further minimize the magnitude of the nearest side-lobe in the frequency r

(window_len, symmetric=False)

def blackman_harris(window_len, symmetric=False):
    """
    The Blackman-Harris window.

    Notes
    -----
    The Blackman-Harris window is an instance of the more general class of
    cosine-sum windows where `K=3`. Additional coefficients extend the Hamming
    window to further minimize the magnitude of the nearest side-lobe in the
    frequency response.

    .. math::
        \\text{bh}(n) = a_0 - a_1 \cos\left(\\frac{2 \pi n}{N}\\right) +
            a_2 \cos\left(\\frac{4 \pi n }{N}\\right) -
                a_3 \cos\left(\\frac{6 \pi n}{N}\\right)

    where `N` = `window_len` - 1, :math:`a_0` = 0.35875, :math:`a_1` = 0.48829,
    :math:`a_2` = 0.14128, and :math:`a_3` = 0.01168.

    Parameters
    ----------
    window_len : int
        The length of the window in samples. Should be equal to the
        `frame_width` if applying to a windowed signal.
    symmetric : bool
        If False, create a 'periodic' window that can be used in with an FFT /
        in spectral analysis.  If True, generate a symmetric window that can be
        used in, e.g., filter design. Default is False.

    Returns
    -------
    window : :py:class:`ndarray <numpy.ndarray>` of shape `(window_len,)`
        The window
    """
    return generalized_cosine(
        window_len, [0.35875, 0.48829, 0.14128, 0.01168], symmetric
    )


def hamming(window_len, symmetric=False):