Research On Frequency Estimation Algorithm Of Sinusoidal Signal Based On DFT

Estimating the frequency of a sinusoidal signal embedded in Gaussian white noise is not only an important research content of modern digital signal processing,but also has been widely used in many practical engineering fields such as mobile communication and power quality monitoring.Studying the frequency estimation technology of noisy sinusoidal signals has notable theoretical significance and application value.Discrete Fourier transform(DFT)is a widely recognized frequency estimation method due to its intuitive physical meaning and simple implementation.However,inherent defects such as spectrum leakage make it requires additional steps to improve the performance.DFT-based frequency estimation algorithms of sinusoidal signals are studied in this paper and the specific research work completed includes:Firstly,the basic theory of frequency estimation is studied,and the mathematical model of sinusoidal signal frequency estimation is established.On this basis,the estimation errors caused by inherent defects of of DFT estimator are explained.Then the theoretical lower bound CRLB of sinusoidal signals frequency estimation mean square error is derived from the perspective of probability theory,which is the target of frequency estimation algorithms.Secondly,the existing DFT-based frequency estimation algorithms are introduced and studied.The frequency estimator based on frequency domain transformation can be classified into two categories Interpolated DFT(IpDFT)and Smart DFT(SDFT).The IpDFT algorithm performs frequency estimation by the differences between the adjacent frequency components at the same time instant,while SDFT-based algorithm extracts frequency based on the same DFT component of the signal sequences at different times.Derivation and simulation show that the two types of estimators can effectively improve the spectrum leakage problem in DFT transform,but still have some room for improvement under serious spectrum leakage.Thirdly,two new IpDFT algorithms considering the spectrum leakage of negative frequency component of real-valued sinusoidal signals are proposed to solve the spectrum leakage problem.Based on the interpolation proportional relationship between the real or imaginary part of the peak spectral and its adjacent component,the first IpDFT algorithm selects the interpolation relationship between them according to the absolute value of the real and imaginary part of the peak spectrum.The other method superimposes the real and imaginary ratios to form a new interpolation scale factor.The long-range leakage of the negative frequency component is completely considered and sloved in the two proposed IpDFT methods,which means they have extremely high estimation accuracy and good rejection capability of image component interference.Simulation results demonstrate the benefits of the proposed algorithm,especially under serious spectrum interference,the superiority is more significant.Then,the differences between the same DFT frequency component of signal at adjacent time instants is studied and an efficient frequency estimator based on the same sliding-window DFT components at two continuous start time is proposed.Computer simulations prove that the advantage of the algorithm in resisting spectrum leakage.Compared with the classical SDFT estimation scheme with similar principle,the proposed algorithm has great performance improvement,whose frequency estimation accuracy is similar to CLS-SDFT without solving the overdetermined equation.The superiority of frequency estimation is more obvious than the IpDFT algorithm and the original SDFT algorithm,especially for sinusoidal signals with closely spaced positive and negative frequency components.In the presence of higher harmonic interference,the algorithm still maintains the lead in estimating accuracy.Finally,an extended multi-frequency complex sinusoidal frequency estimation scheme is proposed based on the linear prediction relationship between the same DFT spectral components in the continuous time,which is also applicable to the single real-valued sinusoidal signal.Simulation and experimental results show that the proposed algorithm has higher estimation accuracy and anti-noise performance than the existing estimators.When the signal degenerates into a real-valued sinusoidal signal that is mainly studied in this paper,the proposed scheme can also provide accurate frequency estimation results.