Understanding the PRBS signal as an optimum input signal in the wavelet-correlation method of system identification using multiresolution analysis

This paper will focus on the relationship between the pseudo-random binary sequence (PRBS) signal and the dyadic lattice. A method for estimating the PRBS function by a series of Haar wavelets is derived and explained. Relating the PRBS signal to the Haar wavelet is advantageous because the Haar wavelet forms an orthonormal wavelet basis. Multiresolution analysis is used to write the PRBS signal as a finite series of Haar wavelets, and the dyadic period of the PRBS signal is exploited to make this task easier. The PRBS signal and dyadic lattice are shown to be complimentary choices for the wavelet-correlation (W-C) method.