Method for estimating sinusoidal signal frequency based on DFT

Abstract

The invention discloses a method for estimating the sinusoidal signal frequency based on DFT. The method aims to achieve that root-mean-square errors of frequency estimation are all similar to a cramer-rao lower limit when relative frequency deviation is an arbitrary value, and the estimation performance of the method is superior to that of an existing frequency estimation algorithm. Through analysis of the performance of a Candan algorithm and the performance of a 2N point DFT algorithm, after necessary discretization preprocessing is conducted on original signals, frequency deviation is estimated through the Candan algorithm in the coarse estimation stage, and the frequency of the original signals is corrected through the frequency deviation; then fine estimation is conducted on the corrected original signals through the 2N point DFT algorithm. The step for correcting the frequency of the original signals is added, the advantages of the Candan algorithm and the advantages of the 2N point DFT algorithm are exerted, and the method is very suitable for application occasions with high estimation accuracy requirements.

Description

technical field [0001] The invention belongs to signal processing technology, and relates to technical fields such as communication, radar, sonar and electronic countermeasures. Background technique [0002] Frequency estimation of sinusoidal signals under noisy conditions is a classic topic in signal processing. In recent years, because the frequency estimation algorithm based on DFT (Discrete Fourier Transform, DFT for short) has the advantages of fast operation speed, significant signal-to-noise ratio gain for sinusoidal signals, and insensitivity to algorithm parameters, so such Algorithms have received more and more attention from domestic scholars. [0003] The DFT-based frequency estimation algorithm is divided into two steps: rough estimation and fine estimation. In the rough estimation stage, the DFT transform is performed on the signal, and the position corresponding to the maximum value of the spectrum peak is used as the rough estimation value of the frequency....

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Problems solved by technology

However, since the influence of noise on the signal is ignored in the derivation process of the algorithm, when |δ| is small, the magnitudes of the second largest spectral line in the main lobe and the third largest spectral line in the first side lobe may judge Wrong, resulting in wrong direction of interpolation, resulting in a large error

[0006] The 2N-point DFT frequency estimation algorithm was proposed by Fang Luoyang in 2012 [FangLuoyang, Duan Dongliang and Yang Liuqing, "A new DFT-based frequency estimator for single-tone complex sinusoidal signals[C]," 2012-MILCOM2012.IEEE, Orlando, FL,Oct.2012], the algorithm makes more spectral lines in the main lobe of the signal spectrum by performing 2N-point DFT transformation on the signal. When the real frequency of the signal is close to the maximum spectral peak of the DFT transformation, that is, at the When the deviation is small, |X[k m -1]| and |X[k m +1]| has a large value and is less affected by noise interference, so that higher estimation accuracy can be obtained, and the estimated variance is close to CRLB (Cramer‐Rao lower bound, CRLB for short); but the method The disadvantage is that when the signal frequency deviation is large, |X[k m -1]| and |X[k m +1]|One of them will be reduced, the influence of noise interference will become larger, the estimation accuracy will be reduced, and the frequency estimation variance will deviate from CRLB

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