Module « scipy.signal »

Fonction max_len_seq - module scipy.signal

Signature de la fonction max_len_seq

def max_len_seq(nbits, state=None, length=None, taps=None) 

Description

max_len_seq.__doc__

    Maximum length sequence (MLS) generator.

    Parameters
    ----------
    nbits : int
        Number of bits to use. Length of the resulting sequence will
        be ``(2**nbits) - 1``. Note that generating long sequences
        (e.g., greater than ``nbits == 16``) can take a long time.
    state : array_like, optional
        If array, must be of length ``nbits``, and will be cast to binary
        (bool) representation. If None, a seed of ones will be used,
        producing a repeatable representation. If ``state`` is all
        zeros, an error is raised as this is invalid. Default: None.
    length : int, optional
        Number of samples to compute. If None, the entire length
        ``(2**nbits) - 1`` is computed.
    taps : array_like, optional
        Polynomial taps to use (e.g., ``[7, 6, 1]`` for an 8-bit sequence).
        If None, taps will be automatically selected (for up to
        ``nbits == 32``).

    Returns
    -------
    seq : array
        Resulting MLS sequence of 0's and 1's.
    state : array
        The final state of the shift register.

    Notes
    -----
    The algorithm for MLS generation is generically described in:

        https://en.wikipedia.org/wiki/Maximum_length_sequence

    The default values for taps are specifically taken from the first
    option listed for each value of ``nbits`` in:

        https://web.archive.org/web/20181001062252/http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm

    .. versionadded:: 0.15.0

    Examples
    --------
    MLS uses binary convention:

    >>> from scipy.signal import max_len_seq
    >>> max_len_seq(4)[0]
    array([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=int8)

    MLS has a white spectrum (except for DC):

    >>> import matplotlib.pyplot as plt
    >>> from numpy.fft import fft, ifft, fftshift, fftfreq
    >>> seq = max_len_seq(6)[0]*2-1  # +1 and -1
    >>> spec = fft(seq)
    >>> N = len(seq)
    >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')
    >>> plt.margins(0.1, 0.1)
    >>> plt.grid(True)
    >>> plt.show()

    Circular autocorrelation of MLS is an impulse:

    >>> acorrcirc = ifft(spec * np.conj(spec)).real
    >>> plt.figure()
    >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')
    >>> plt.margins(0.1, 0.1)
    >>> plt.grid(True)
    >>> plt.show()

    Linear autocorrelation of MLS is approximately an impulse:

    >>> acorr = np.correlate(seq, seq, 'full')
    >>> plt.figure()
    >>> plt.plot(np.arange(-N+1, N), acorr, '.-')
    >>> plt.margins(0.1, 0.1)
    >>> plt.grid(True)
    >>> plt.show()