`scipy.signal._max_len_seq:max_len_seq`

source: /scipy/signal/_max_len_seq.py:22

Signature

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

Summary

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

Examples

MLS uses binary convention:

from scipy.signal import max_len_seq
max_len_seq(4)[0]

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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)

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plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')

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[<matplotlib.lines.Line2D object at 0x7fa8f406eba0>]

plt.margins(0.1, 0.1)
plt.grid(True)
plt.show()

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Circular autocorrelation of MLS is an impulse:

acorrcirc = ifft(spec * np.conj(spec)).real

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plt.figure()
plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')

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[<matplotlib.lines.Line2D object at 0x7fa8f406d6a0>]

plt.margins(0.1, 0.1)
plt.grid(True)
plt.show()

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Linear autocorrelation of MLS is approximately an impulse:

acorr = np.correlate(seq, seq, 'full')

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plt.figure()
plt.plot(np.arange(-N+1, N), acorr, '.-')

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[<matplotlib.lines.Line2D object at 0x7fa8fe7ebe00>]

plt.margins(0.1, 0.1)
plt.grid(True)
plt.show()

✓