Estimation of parameters of the weakly damped sinusoidal signals in the frequency domain

In this paper, exponentially damped sinusoidal signals are analyzed. Simple algorithms for fast measurement and estimation of the unknown damping, frequency, amplitude and phase are presented. The peaks of the discrete Fourier transform (DFT) results are adopted to obtain the parameters. The concept of quotient interpolation using the Hann window for the basic three parameters is also adopted for the damping estimation. In the case of the weakly damped sinusoids with dumping values up to 1, using the rectangular window in the estimation reduces the systematic errors in comparison with the Hann window, especially in the vicinity of the coherent sampling conditions.