{'fraction_non_alphanumeric': 0.03138075313807531, 'fraction_numerical': 0.0, 'mean_word_length': 5.095541401273885, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Steady-state performance analysis of the LMS adaptive time-varying second order Volterra filter

In this paper, the steady-state performance of the Least Mean Square (LMS) adaptive second order Volterra filter, with constant step-sizeμ, in a time-varying setting, is analysed. The quantitative evaluation of the steady-state Excess Mean Square Error (EMSE), where the contribution of the gradient misadjustment and the tracking error are well characterized, is established. The optimum step-size for time-varying second order Volterra filter is then given. Thus, we can study the correlation between the Excess MSE and the optimum step-size in one hand and the parameters of the time-varying nonlinear system, in the other hand. Furthermore, the steady-state behavior predicted by the analysis is in good agreement with the experimental results. The adaptive filter was used in a second order Volterra system identification in a non stationary environment.