max_len_seq(nbits, state=None, length=None, taps=None)
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
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.
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.
Number of samples to compute. If None, the entire length (2**nbits) - 1
is computed.
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
).
Resulting MLS sequence of 0's and 1's.
The final state of the shift register.
Maximum length sequence (MLS) generator.
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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._max_len_seq.max_len_seq
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