Research On Parameter Estimation Algorithms Of Real Sinusoidal Signals Based On DFT

Sinusoidal signal parameter estimation is a basic problem in digital signal processing,and has been applied in biomedical signal processing,radar analysis,power failure detection,and speech recognition.In the actual engineering system,most of the obtained sinusoidal signals are interfered by noise or higher harmonics.How to extract frequency,phase and other parameters from noisy sinusoidal signals has also become a current research hotspot.Existing parameter estimation methods can be roughly divided into two categories: time-domain methods and frequency-domain methods.Time-domain methods are generally based on parametric modeling.Although this method is easy to understand,the computational complexity is high.DFT transform has become the first choice for frequency domain estimation algorithms due to its simple implementation and low computational cost.However,DFT transform has inherent defects such as spectral leakage and fence effect.When the signal does not satisfy coherent sampling or the signal frequency is low,the estimated performance will be Great influence.In order to suppress the impact of spectrum leakage and improve the estimation accuracy and anti-noise performance of the estimator,this paper expands the research on the parameter estimation of noisy sinusoidal signals.The main research work includes:Firstly,a novel adaptive frequency estimator based on DFT is proposed.The basic idea of the algorithm is to use the two largest DFT coefficients to construct a nonlinear equation describing the relationship between the DFT coefficients and the system frequency based on the spectral peak search to obtain the rough frequency estimation results,and then iteratively adaptive The method finds the system frequency with minimal error.Since the proposed algorithm uses only two DFT coefficients,the amount of calculation is reduced.And the algorithm fully considers and calculates the spectrum leaked from the negative frequency,so it has strong anti-spectrum leakage interference ability.The simulation results show that the proposed algorithm has good anti-noise and harmonic interference capabilities,and has better instantaneous convergence than the comparison algorithm.Secondly,a three-point IpDFT method based on the superposition of positive and negative frequency spectra is proposed.The basic idea of the algorithm is to obtain a rough estimate of the frequency,and use the spectral line values at and to interpolate to obtain a fine estimate of the frequency.The proposed algorithm fully takes into account the long-range leakage of negative frequency components during the derivation process,so that the problem of spectrum leakage caused by the time-domain truncation of the signal can be fully resolved,so the algorithm has extremely high estimation accuracy and resistance to negative frequency component interference Ability.Simulation experiment results show that the new IpDFT scheme proposed in this chapter can accurately estimate the frequency of real sinusoidal signals,and the mean square error of the estimated results is close to CRLB.Finally,a phase difference estimation algorithm based on DFT is proposed.The main idea of the proposed algorithm is to use the proposed three-point IpDFT method based on the superposition of positive and negative spectrum to estimate the angular frequency of the signal,and on this basis,calculate the phase difference between the two signals.If the signal frequency is known,the proposed method can obtain an accurate estimate of the initial phase.And when the frequency is very low or close to the Nyquist frequency,or when there is not enough sample data for DFT calculation,the performance of the algorithm is also considerable.Simulation results show that the proposed algorithm has good anti-noise performance.