SYSTEM-IDENTIFICATION WITH PERFECT SEQUENCES BASED ON THE NLMS ALGORITHM

The problem of measuring the impulse response of an unknown linear tra nsmission system has been studied within many papers. One approach for the identification problem represents the so called fast M-sequence t ransform, where a binary periodic maximal-length sequence is used as e xcitation signal for the unknown system. This identification process b ases on the cross correlation between one period of the maximal-length sequence and its received system response. In this paper an alternati ve to several existing approaches is proposed by using a periodic perf ect sequence stimulus signal for the normalized least mean square (NLM S) algorithm. In contrast to the normally used stochastic white noise process with this deterministic excitation signal the NLMS algorithm i s capable to identify a linear noiseless system within one period. Sev eral theoretical aspects of this technique will be discussed. Consider ing that in many applications such as acoustic echo compensation, acou stic feedback control or active noise reduction the NLMS algorithm is applied, the practical point of view of the proposed method becomes ap parent.