Function generalized_cosine

numpy_ml/utils/windows.py:108–142

The generalized cosine family of window functions. Notes ----- The generalized cosine window is a simple weighted sum of cosine terms. For :math:`n \in \{0, \ldots, \\text{window_len} \}`: .. math:: \\text{GCW}(n) = \sum_{k=0}^K (-1)^k a_k \cos\left(\\frac{2 \pi

(window_len, coefs, symmetric=False)

def generalized_cosine(window_len, coefs, symmetric=False):
    """
    The generalized cosine family of window functions.

    Notes
    -----
    The generalized cosine window is a simple weighted sum of cosine terms.

    For :math:`n \in \{0, \ldots, \\text{window_len} \}`:

    .. math::

        \\text{GCW}(n) = \sum_{k=0}^K (-1)^k a_k \cos\left(\\frac{2 \pi k n}{\\text{window_len}}\\right)

    Parameters
    ----------
    window_len : int
        The length of the window in samples. Should be equal to the
        `frame_width` if applying to a windowed signal.
    coefs: list of floats
        The :math:`a_k` coefficient values
    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
    """
    window_len += 1 if not symmetric else 0
    entries = np.linspace(-np.pi, np.pi, window_len)  # (-1)^k * 2pi*n / window_len
    window = np.sum([ak * np.cos(k * entries) for k, ak in enumerate(coefs)], axis=0)
    return window[:-1] if not symmetric else window


class WindowInitializer: