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# scipy.signal.max_len_seq

scipy.signal.max_len_seq(nbits, state=None, length=None, taps=None)

  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

  New in version 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 numpy as np
      >>> 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()