max_len_seq#
- scipy.signal.max_len_seq(nbits, state=None, length=None, taps=None)[source]#
- Maximum length sequence (MLS) generator. - Parameters:
- nbitsint
- 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.
- statearray_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- stateis all zeros, an error is raised as this is invalid. Default: None.
- lengthint, optional
- Number of samples to compute. If None, the entire length - (2**nbits) - 1is computed.
- tapsarray_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:
- seqarray
- Resulting MLS sequence of 0’s and 1’s. 
- statearray
- The final state of the shift register. 
 
 - Notes - The algorithm for MLS generation is generically described in: - The default values for taps are specifically taken from the first option listed for each value of - nbitsin:- Added in version 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() 