A Note on Optimality of Analytical Leakage Compensation at Boundary Frequencies

The interpolated fast Fourier transform (IFFT) was one of the first methods for the highly accurate estimation of sine wave parameters, and its first successful descendant was analytical leakage compensation [which is commonly called analytical solution (AS)]. The AS estimate of frequency is a whole class of solutions whose variance depends on a free parameter K. Thus, to extract the minimum variance solution from a theoretically infinite set, we have to find the optimal value K _opt. This paper clarifies the mathematical background of AS and proposes two new solutions for K _opt, which reduce the variance of AS estimates of low and high frequencies close to an integer. All inferences are justified by simulations, which confirm the validity of theoretical considerations.