Algorithms for Real-Valued Noisy Damped Sinusoid Parameter Estimation

Abstract

In this article, an improved version of three state-of-the-art interpolated discrete-time Fourier transform (IpDTFT) algorithms for the estimation of the frequency and the damping factor of noisy damped sinusoids is proposed. Sinusoid amplitude and phase are also estimated. Improvement is obtained by both compensating the effect on the estimated parameters of the spectral leakage from the fundamental image component and minimizing the estimator variance through a suitable selection of the interpolation points. The obtained estimates are then further improved by applying a linear signal fit (LSF) algorithm. The accuracies of the proposed algorithms are compared with each other and with the related Cramér–Rao lower bound through computer simulations. The required computational times are also briefly analyzed in order to assess the algorithms usefulness in real-time applications.

Keywords

• Algorithms
• discrete Fourier transforms (DFTs)
• error analysis
• least-squares methods
• parameter estimation
• signal processing