Ticket #581: chebwin.py

def chebwin(M, at, sym=1):
    """Dolph-Chebyshev window.

    INPUTS:

      M : int
        Window size
      at : float
        Attenuation (in dB)
      sym : bool
        Generates symmetric window if True.

    """
    if M < 1:
        return array([])
    if M == 1:
        return ones(1,'d')

    odd = M % 2
    if not sym and not odd:
        M = M+1

    # compute the parameter beta
    beta = cosh(1.0/(M-1.0)*arccosh(10**(abs(at)/20.)))
    k = r_[0:M]*1.0
    x = beta*cos(pi*k/M)
    # find the window's DFT coefficients
    # using the Chebyshev polynomial
    p = polyval(special.chebyt(M - 1), x)
    # Appropriate IDFT and filling up
    # depending on even/odd M
    if M % 2:
        w = real(fft(p * 1.0));
        n = (M + 1) / 2;
        w = w[:n] / w[0];
        w = numpy.core.concatenate((w[n - 1:0:-1], w))
    else:
        p = p * exp(1.j*pi / M * r_[0:M])
        w = real(fft(p));
        n = M / 2 + 1;
        w = w / w[1];
        w = numpy.core.concatenate((w[n - 1:0:-1], w[1:n]));
    if not sym and not odd:
        w = w[:-1]
    return w