A New Hybrid Method for Signal Estimation Based on Haar Transform and Prony Analysis

The signal estimation is very important in electrical and electronic engineering. In this study, it is shown that signal parameters' (frequency, amplitude, and phase) estimation can be realized with the implementation of Prony method on Haar transform coefficients. In order to accomplish this, mathematical relationship between roots of Prony polynomial which are found with original signal values and roots which are calculated with Haar approximation/detail coefficients is constructed. Frequency components of signal are estimated with this relationship. Next, the second part of Prony algorithm which constructs the matrix equation between roots and signal values in order to find the amplitude and phase values is implemented with Haar coefficients. In other words, a new matrix equation is derived for finding amplitudes and phases with the found roots in the first step and Haar coefficients. Thus, implementations of the first and second steps give signal parameters. Derived equations are valid for all degrees of Haar coefficients not just the first one. The use of Haar coefficients decreases the data size and increases the speed and accuracy. The proposed method is also more robust of selection of different Prony polynomial coefficient sizes.