Research On Frequency Estimation Of Real Sinusoidal Signals Based On DFT

Frequency measurement of a real sine-wave is not only an important research project in the modern digital signal processing,but also has a wide range of applications in military and civilian radar systems,communication systems,biomedicine and other fields.Therefore,it is of great theoretical significance and practical value to the study of real sinusoidal frequency estimation under white Gaussian noise environment.Moreover,the discrete Fourier transform(DFT)has gradually become one of the important research directions because of its intuitive and clear physical meaning and small calculation amount.In this paper,Interpolated DFT(IpDFT)and Smart DFT(SDFT)related algorithms are studied,and it is found that DFT has fence effect and spectrum leakage.In the real sinusoidal signal model with close positive and negative frequency distribution,the impact of this defect is particularly prominent.In response to this problem,frequency estimation algorithm based on DFT for real sinusoidal signal is studied.First of all,the differences between the same DFT frequency component of real sinusoidal signal at different time instants is studied.Based on the same sliding-window DFT components,the efficient frequency estimator is implemented by the proportional relationship between the real and imaginary components.For the problem of singularities in direct applications,the delay sliding window is applied to optimize.The theoretical performance of the algorithm is analyzed in the case of noise.The simulation results match well with the theoretical values.In addition,computer simulations demonstrate that the proposed algorithm reduces spectral leakage and provides good noise and harmonic suppression capability.Based on the above algorithm,the Maximum sidelobes decaying(MSD)window and triangular self-convolution window(TSCW)with good sidelobe performance are selected to reduce spectral leakage and fence effects caused by DFT of signals with asynchronous sampling and non-integer period truncation.Frequency estimation is performed for even and odd cases when the real and imaginary part is fully considered.The simulation results match well with the theoretical values.In addition,computer simulations demonstrate that the proposed algorithm provides better noise and harmonic suppression capability than other algorithms.At the same time,the relationship between different DFT frequency components at different times of the real sinusoidal signal is studied.The maximum and second largest spectral lines at different times are selected for frequency estimation.A univariate cubic equation about frequency is established by the proportional relationship of the imaginary and real parts between the largest spectral line at the previous time instant and second-largest spectral line at the later.And then three sets of frequency values to be estimated are obtained.Similarly,other three sets are obtained by the remaining two spectral lines.At last,the estimated frequency are accurately extracted from two sets of candidate values without expanding the length of the real sine signal sequence.The performances of sine and harmonic signals are studied and the overall performance is better than other algorithms.