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1# Author: Eric Larson
2# 2014
4"""Tools for MLS generation"""
6import numpy as np
8from ._max_len_seq_inner import _max_len_seq_inner
10__all__ = ['max_len_seq']
13# These are definitions of linear shift register taps for use in max_len_seq()
14_mls_taps = {2: [1], 3: [2], 4: [3], 5: [3], 6: [5], 7: [6], 8: [7, 6, 1],
15 9: [5], 10: [7], 11: [9], 12: [11, 10, 4], 13: [12, 11, 8],
16 14: [13, 12, 2], 15: [14], 16: [15, 13, 4], 17: [14],
17 18: [11], 19: [18, 17, 14], 20: [17], 21: [19], 22: [21],
18 23: [18], 24: [23, 22, 17], 25: [22], 26: [25, 24, 20],
19 27: [26, 25, 22], 28: [25], 29: [27], 30: [29, 28, 7],
20 31: [28], 32: [31, 30, 10]}
22def max_len_seq(nbits, state=None, length=None, taps=None):
23 """
24 Maximum length sequence (MLS) generator.
26 Parameters
27 ----------
28 nbits : int
29 Number of bits to use. Length of the resulting sequence will
30 be ``(2**nbits) - 1``. Note that generating long sequences
31 (e.g., greater than ``nbits == 16``) can take a long time.
32 state : array_like, optional
33 If array, must be of length ``nbits``, and will be cast to binary
34 (bool) representation. If None, a seed of ones will be used,
35 producing a repeatable representation. If ``state`` is all
36 zeros, an error is raised as this is invalid. Default: None.
37 length : int, optional
38 Number of samples to compute. If None, the entire length
39 ``(2**nbits) - 1`` is computed.
40 taps : array_like, optional
41 Polynomial taps to use (e.g., ``[7, 6, 1]`` for an 8-bit sequence).
42 If None, taps will be automatically selected (for up to
43 ``nbits == 32``).
45 Returns
46 -------
47 seq : array
48 Resulting MLS sequence of 0's and 1's.
49 state : array
50 The final state of the shift register.
52 Notes
53 -----
54 The algorithm for MLS generation is generically described in:
56 https://en.wikipedia.org/wiki/Maximum_length_sequence
58 The default values for taps are specifically taken from the first
59 option listed for each value of ``nbits`` in:
61 http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm
63 .. versionadded:: 0.15.0
65 Examples
66 --------
67 MLS uses binary convention:
69 >>> from scipy.signal import max_len_seq
70 >>> max_len_seq(4)[0]
71 array([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=int8)
73 MLS has a white spectrum (except for DC):
75 >>> import matplotlib.pyplot as plt
76 >>> from numpy.fft import fft, ifft, fftshift, fftfreq
77 >>> seq = max_len_seq(6)[0]*2-1 # +1 and -1
78 >>> spec = fft(seq)
79 >>> N = len(seq)
80 >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')
81 >>> plt.margins(0.1, 0.1)
82 >>> plt.grid(True)
83 >>> plt.show()
85 Circular autocorrelation of MLS is an impulse:
87 >>> acorrcirc = ifft(spec * np.conj(spec)).real
88 >>> plt.figure()
89 >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')
90 >>> plt.margins(0.1, 0.1)
91 >>> plt.grid(True)
92 >>> plt.show()
94 Linear autocorrelation of MLS is approximately an impulse:
96 >>> acorr = np.correlate(seq, seq, 'full')
97 >>> plt.figure()
98 >>> plt.plot(np.arange(-N+1, N), acorr, '.-')
99 >>> plt.margins(0.1, 0.1)
100 >>> plt.grid(True)
101 >>> plt.show()
103 """
104 if taps is None:
105 if nbits not in _mls_taps:
106 known_taps = np.array(list(_mls_taps.keys()))
107 raise ValueError('nbits must be between %s and %s if taps is None'
108 % (known_taps.min(), known_taps.max()))
109 taps = np.array(_mls_taps[nbits], np.intp)
110 else:
111 taps = np.unique(np.array(taps, np.intp))[::-1]
112 if np.any(taps < 0) or np.any(taps > nbits) or taps.size < 1:
113 raise ValueError('taps must be non-empty with values between '
114 'zero and nbits (inclusive)')
115 taps = np.ascontiguousarray(taps) # needed for Cython
116 n_max = (2**nbits) - 1
117 if length is None:
118 length = n_max
119 else:
120 length = int(length)
121 if length < 0:
122 raise ValueError('length must be greater than or equal to 0')
123 # We use int8 instead of bool here because NumPy arrays of bools
124 # don't seem to work nicely with Cython
125 if state is None:
126 state = np.ones(nbits, dtype=np.int8, order='c')
127 else:
128 # makes a copy if need be, ensuring it's 0's and 1's
129 state = np.array(state, dtype=bool, order='c').astype(np.int8)
130 if state.ndim != 1 or state.size != nbits:
131 raise ValueError('state must be a 1-D array of size nbits')
132 if np.all(state == 0):
133 raise ValueError('state must not be all zeros')
135 seq = np.empty(length, dtype=np.int8, order='c')
136 state = _max_len_seq_inner(taps, state, nbits, length, seq)
137 return seq, state