Determination of amplitude levels of the piecewise constant signal by using polynomial approximation

A new approach to determining the amplitude levels of piecewise constant signal has been proposed that is based on using its multiplicative model and solving the problem of polynomial approximation. In case of the absence of noise, the statement of polynomial approximation problem is based on the requirement of exact match of the current signal value with the amplitude value of one of its levels. In case of the presence of ordinary additive noise, the problem statement is based on the least squares criterion, while the solution of problem is presented in the analytical form. For the case of the presence of pulse-type noise, the problem statement is based on the minimum duration criterion, while the problem solution is achieved numerically by an appropriate functional minimization in unknown amplitudes of levels. The case of binary piecewise constant signal is considered in detail. The results of numerical simulation are presented for the cases, where the binary signal is distorted by ordinary additive noise with Gaussian distribution law and the pulse-type noise with the Cauchy distribution law.