Damped sinusoidal signals parameter estimation in frequency domain

Parameter estimation of noisy damped sinusoidal signals in the frequency domain is presented in this paper. The advantage of the frequency domain approach is having the spectral energy concentrated in frequency domain samples. However, the least squares criterion for frequency estimation using frequency domain samples is nonlinear. A low complexity three-sample estimation algorithm (TSEA) for solving the nonlinear problem is proposed. Using the TSEA for initialization, a frequency domain nonlinear least squares (FD-NLS) estimation algorithm is then proposed. In the case of white Gaussian noise, it yields maximum likelihood estimates, verified by simulation results. A time domain NLS (TD-NLS) estimation algorithm is also proposed for comparison.The Cramer–Rao lower bound (CRLB) of the frequency domain estimation algorithms is derived. The theoretical analysis shows that the FD-NLS can yield a near-optimal performance with few energy-concentrated samples. On the other hand, the TD-NLS does not have the energy concentration property and requires more time domain samples to perform satisfactory estimation. Simulation results verify that the frequency domain estimation algorithms provide better tradeoff between computational complexity and estimation accuracy than time domain algorithms.

► Parameter estimation of noisy damped sinusoidal signals in the frequency domain is presented.
► A low complexity frequency domain three-sample estimation algorithm (TSEA) is proposed.
► A high performance frequency domain nonlinear least squares (FD-NLS) estimation algorithm is proposed.
► The Cramer–Rao lower bound (CRLB) of the frequency domain estimation algorithms is derived.
► The theoretical analysis shows that the FD-NLS can yield a near-optimal performance with few energy-concentrated samples.