U Hv fÆã!@sÚdZddlZddlmZdgZdgdgdgdgdgd gd d dgdgd gd gd d dgdd dgdddgdgdddgdgd gdddgdgdgdgdgdddgdgdddgdddgdgdgdd d gd gd!d"d gd#œZd%d$d„ZdS)&zTools for MLS generationéNé)Ú_max_len_seq_innerÚ max_len_seqéééééé é é éé éé ééééééééééééééééé)rrr rrr rr r r rrrrérrrrrrrrrrrrrr!r é cCs„t ¡jdkrtjntj}|dkrf|tkrTt tt ¡ƒ¡}t d|  ¡|  ¡fƒ‚t t||¡}nTt  t ||¡¡ddd…}t  |dk¡s¨t  ||k¡s¨|jdkr°t dƒ‚t |¡}d|d}|dkrÔ|}nt|ƒ}|dkrìt d ƒ‚|dkr tj|tjd d }ntj|td d  tj¡}|jdks:|j|krBt d ƒ‚t |dk¡rZt d ƒ‚tj|tjd d }t|||||ƒ}||fS)a} 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() r Nz/nbits must be between %s and %s if taps is NoneéÿÿÿÿrrzEtaps must be non-empty with values between zero and nbits (inclusive)rz)length must be greater than or equal to 0Úc)ZdtypeÚorderz'state must be a 1-D array of size nbitszstate must not be all zeros)ÚnpZintpÚitemsizeZint32Zint64Ú _mls_tapsÚarrayÚlistÚkeysÚ ValueErrorÚminÚmaxÚuniqueÚanyÚsizeÚintZonesZint8ÚboolZastypeÚndimÚallÚemptyr)ÚnbitsÚstateÚlengthZtapsZ taps_dtypeZ known_tapsZn_maxÚseq©r<ú=/tmp/pip-unpacked-wheel-96ln3f52/scipy/signal/_max_len_seq.pyrs8Sÿ&   )NNN)Ú__doc__Znumpyr'rÚ__all__r)rr<r<r<r=Ús<  ú