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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

help(scipy.signal.max_len_seq)

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 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()

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