System identification and filtering using pseudo random binary inputs

The problem of identifying the impulse response of an unknown system is investigated when the input is restricted to a pseudo random binary sequence (PRBS). The well-known methods, such as the Least Mean Square (LMS) and the Recursive Least Square (RLS) algorithms, are studied for system modeling with a PRBS input and the results are compared. It is shown that post-processing the impulse response with a suitable filter may lead to even better identification. A new post-processing filter, namely, the Med-Mean (MM) filter, is proposed which smoothes the baseline noise of the identified impulse response while preserving the edges.