Fast interpolated DTFT estimators of frequency and damping factor of real-valued damped sinusoids

This paper deals with the estimation of real-valued damped sinusoid frequency and damping factor. To that aim an Interpolated Discrete Time Fourier Transform (IpDTFT) algorithm is proposed which extends to real-valued signal an algorithm proposed in the literature for complex-valued damped sinusoids. The proposed algorithm provides fast estimates of the unknown parameters of either undistorted or distorted real-valued noisy damped sinusoids with accuracy generally better than the one ensured by state-of-the-art estimators, especially when few sinusoid cycles are analysed. Accuracy improvement is obtained by both weighting the acquired signal using a Maximum Sidelobe Decay (MSD) window and compensating the contribution of the spectral image component on the estimated parameters. Analytical expressions for the estimator variances due to wideband noise are also derived.