Parameter Estimation for Exponential Signals by the Quadratic Interpolation

This paper offers a complete method to find the exact frequency, damping, amplitude, and phase of the exponential molds. A simulated signal is taken to fit the real one. When this simulated signal is equal to the real one, the parameters of the simulated signal are identical to the real values. This method includes three major steps, initial value setting, gradient method, and quadratic interpolation. In initial value setting, this method analyzes the mold parameter with the two highest amplitudes of each mold, and the precise values will be found. The difference between simulated and practical signals could be expressed as a least mean square problem. The gradient method provides the initial condition for the quadratic interpolation. The minimum error search is accomplished by the quadratic interpolation, which could improve the search efficiency and reduce iteration time. After a few iterations, the method will obtain the exact harmonic parameters.