Sinusoidal Polynomial Parameter Estimation Using the Distribution Derivative

In this paper, we present a method to estimate the parameters of a generalized sinusoidal model. A generalized sinusoid x is defined as a polynomial in the log domain, with complex coefficients alpha_i : x(t)=exp(Sigma_i alpha_i t ⁱ), where i=0...Q. The method is based on the distribution derivative of the signal and operates in the transform domain. The method is very general and can use any linear transform such as the Fourier transform or the wavelet transform, or even combinations of linear transforms. Examples with the Fourier transform are given. The Fourier-based estimation methods are evaluated using synthetic signals and have performance very close to the theoretical bound.