Generalized multi-point interpolated DTFT frequency and damping factor estimators of real-valued damped sinusoids

In this paper a generalized multi-point interpolated Discrete-Time Fourier Transform (DTFT) is proposed for frequency and damping factor estimation of real-valued damped sinusoids. The acquired data are weighted by a Maximum Sidelobe Decay (MSD) window and the interpolation function is defined as the ratio between two linear combinations of DTFT samples located one bin apart, which is generalized exploiting a tuning parameter. Analytical expressions for the estimated parameter errors due to the interference of the fundamental image component are derived. Leveraging on these expressions an improved version of the algorithm is also proposed and optimized by selecting a suitable value for the tuning parameter. The developed theory is applied to both a three-point and a four-point interpolated Discrete Fourier Transform (IpDFT) estimators published in the literature and the achieved accuracy improvements are verified through simulations.