A solution for the greedy approximation of a step function with a waveform dictionary

In this paper we consider a step function characterized by an arbitrary sequence of real-valued scalars and approximate it with matching pursuit (MP) algorithm. We utilize waveform dictionary rectangular window functions as part show that the is not necessary when all are either non positive or negative parameters wavelet on integer lattice yields closed-form solution for initial optimization problem MP. Additionally, any scalar sequence, provide related at each iteration This allows practical calculation approximating function, which use to examples simulated real univariate time series data display discontinuities in its underlying structure where can be thought sample from signal interest.