Aluode/PerceptionLabPortable

1# Author: Eric Larson
2# 2014
3
4"""Tools for MLS generation"""
5
6import numpy as np
7
8from ._max_len_seq_inner import _max_len_seq_inner
9
10__all__ = ['max_len_seq']
11
12
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]}
21
22def max_len_seq(nbits, state=None, length=None, taps=None):
23    """
24    Maximum length sequence (MLS) generator.
25
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``).
44
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.
51
52    Notes
53    -----
54    The algorithm for MLS generation is generically described in:
55
56        https://en.wikipedia.org/wiki/Maximum_length_sequence
57
58    The default values for taps are specifically taken from the first
59    option listed for each value of ``nbits`` in:
60
61        https://web.archive.org/web/20181001062252/http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm
62
63    .. versionadded:: 0.15.0
64
65    Examples
66    --------
67    MLS uses binary convention:
68
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)
72
73    MLS has a white spectrum (except for DC):
74
75    >>> import numpy as np
76    >>> import matplotlib.pyplot as plt
77    >>> from numpy.fft import fft, ifft, fftshift, fftfreq
78    >>> seq = max_len_seq(6)[0]*2-1  # +1 and -1
79    >>> spec = fft(seq)
80    >>> N = len(seq)
81    >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')
82    >>> plt.margins(0.1, 0.1)
83    >>> plt.grid(True)
84    >>> plt.show()
85
86    Circular autocorrelation of MLS is an impulse:
87
88    >>> acorrcirc = ifft(spec * np.conj(spec)).real
89    >>> plt.figure()
90    >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')
91    >>> plt.margins(0.1, 0.1)
92    >>> plt.grid(True)
93    >>> plt.show()
94
95    Linear autocorrelation of MLS is approximately an impulse:
96
97    >>> acorr = np.correlate(seq, seq, 'full')
98    >>> plt.figure()
99    >>> plt.plot(np.arange(-N+1, N), acorr, '.-')
100    >>> plt.margins(0.1, 0.1)
101    >>> plt.grid(True)
102    >>> plt.show()
103
104    """
105    taps_dtype = np.int32 if np.intp().itemsize == 4 else np.int64
106    if taps is None:
107        if nbits not in _mls_taps:
108            known_taps = np.array(list(_mls_taps.keys()))
109            raise ValueError(f'nbits must be between {known_taps.min()} and '
110                             f'{known_taps.max()} if taps is None')
111        taps = np.array(_mls_taps[nbits], taps_dtype)
112    else:
113        taps = np.unique(np.array(taps, taps_dtype))[::-1]
114        if np.any(taps < 0) or np.any(taps > nbits) or taps.size < 1:
115            raise ValueError('taps must be non-empty with values between '
116                             'zero and nbits (inclusive)')
117        taps = np.array(taps)  # needed for Cython and Pythran
118    n_max = (2**nbits) - 1
119    if length is None:
120        length = n_max
121    else:
122        length = int(length)
123        if length < 0:
124            raise ValueError('length must be greater than or equal to 0')
125    # We use int8 instead of bool here because NumPy arrays of bools
126    # don't seem to work nicely with Cython
127    if state is None:
128        state = np.ones(nbits, dtype=np.int8, order='c')
129    else:
130        # makes a copy if need be, ensuring it's 0's and 1's
131        state = np.array(state, dtype=bool, order='c').astype(np.int8)
132    if state.ndim != 1 or state.size != nbits:
133        raise ValueError('state must be a 1-D array of size nbits')
134    if np.all(state == 0):
135        raise ValueError('state must not be all zeros')
136
137    seq = np.empty(length, dtype=np.int8, order='c')
138    state = _max_len_seq_inner(taps, state, nbits, length, seq)
139    return seq, state
140