The Frequency-domain Parameter Estimation Algorithm Of Exponentially Decaying Sinusoidal Signals

The parameter estimation of exponentially decaying sinusoidal signals in white noise background is a classic subject in the field of digital signal processing,which can be widely used in many fields such as low-frequency mechanical spectroscopy,linear system identifica-tion and nuclear magnetic resonance.However,it is difficult for existing algorithms to be satisfactory in various aspects such as parameter estimation accuracy,algorithm complexity,performance under different signal-to-noise ratios etc.Therefore,the parameter estimation technology of exponentially decaying sinusoidal signals has been continuously concerned by researchers.This thesis investigated the parameter estimation of exponentially decaying sinusoidal signals from three aspects.The main research work done in this thesis is as follows:1)From the perspective of segmented-FFT phase difference,the parameter estimation of exponentially decaying complex sinusoidal signals is discussed,It is proved that the frequency estimation formula of constant amplitude complex sinusoidal signals can still estimate frequency.Meanwhile,estimation formulas of decaying factor,amplitude and initial phase are derived.The segmented-FFT phase difference algorithm has been improved to solve the problem of severe performance degradation when the signal frequency is near an odd multiple of the frequency resolution.Then,root mean square error formulas of frequency and decaying factor are derived.Finally,an improved algorithm combining segmented-phase difference algorithm and A&M algorithm is proposed which has well solved the effect of frequency deviation on parameter estimation.The performance of the proposed algorithm is close to the Cramer-Rao lower bound and is same as A&M algorithm with two iterations,but the complexity of the proposed algorithm is lower.2)From the perspective of three-spectral-line interpolation,the parameter estimation of exponentially decaying complex sinusoidal signals is discussed.A FFT-DTFT algorithm is proposed.Estimation formulas of frequency,decaying factor,amplitude and initial phase,root mean square error formulas of frequency and decaying factor are derived.Then,iterative procedures are used to further improve the algorithm performance.The performance of the proposed algorithm is compared with the algorithm proposed in the previous part of the thesis.Meanwhile,suggestions on how to choose auxiliary spectral lines reasonably in practical applications are given.The algorithm can cover estimation results of parameter when selected spectral lines change anywhere in the main lobe and nearby which is more general.3)From the perspective of spectral cancellation and hanning window,the parameter estimation of exponentially decaying real sinusoidal signals is discussed.The BY1 algorithm and the A&M algorithm with haning window are proposed.Estimation formulas of frequency,decaying factor,amplitude and phase,root mean square error formulas of frequency and decaying factor are derived.Meanwhile these algorithms are compared with the two algorithms proposed in the previous parts of the thesis based on spectrum cancellation.Simulation results show that the performancc of algorithms based on spectrum cancellation is better than algorithms with hanning window in general.At a high signal-to-noise ratio,the algorithm based on spectrum cancellation needs to increase the number of times of spectrum cancellation for maintaining the performance advantage.