New Diserete Spectrum Correetion Approaches And Their Capabilities Against Interference

Spectrum analysis technology has been widely used in various areas, such as mechanical equipment fault diagnosis, vibration analysis, communication engineering, automatic control engineering, radar, sonar, telemetering, remote sensing, image processing, speech recognition, oil exploration, marine resources survey, and biomedical engineering. Due to spectral leakage effect and picket fence effect of the discrete Fourier transform, significant bias would be introduced into the estimates of frequency, amplitude, and in particular, phase, if the sample frame is not an integer multiple of signal period. In practical engineering application, spectrum analysis is often only a qualitative approach rather than a quantitative one to solve the problems, which greatly limits the application of spectrum analysis technology. Therefore, the study on improving the precision of frequency spectrum analysis is one of the main tasks in modern signal processing.The discrete spectrum correction method is a technology, with which more accurate spectral parameters can be obtained by analyzing the amplitude information or phase information of the spectral lines in windowed discrete spectrum. In engineering applications, the discrete spectrum correction methods have been widely used in harmonic analysis and the measurement of electric parameters in power system, radar speed detection, the identification of engine excitation forces and torsional vibration characteristics, fault diagnosis of rotating machinery and so on. As a result, the study of discrete spectrum correction methods is of great importance for engineering practice.Starting from the fast Fourier transform, this paper aims to improve the accuracy of discrete spectrum analysis. Based on the in-depth study of the traditional discrete spectrum correction algorithm and the systematical analysis of factors affecting the accuracy of the discrete spectral correction algorithm, new spectral correction algorithms has been put forward to deal with the existing problems of traditional correction algorithms.Firstly, the phase difference method based on asymmetric windows is proposed. Accurate parameters can be obtained through the same section of data with different asymmetric windows(or an asymmetric window and a symmetric window). This is different from the traditional phase difference methods which require two sections to obtain phase difference. Then, the new concept, barycenter of a window function, is proposed to explain the basic theory of the phase difference methods. The relationship between the linear component of phase line and the barycenter of window function is successfully derived. Besides, the construction methods of asymmetric window functions are also systematically summarized, and the method of translation of window peak put forward in this pater. The most significant feature of this method is that it is possible for one to adjust the amplitude and phase characteristic continuously. In addition, the amplitude and phase characteristics of asymmetric windows are studied, and the characteristics of symmetric windows and asymmetric windows compared in this paper.Secondly, in order to solve the problem of window function dependence in operations with traditional interpolation methods, a new three-line interpolation method is put forward. Based on the characteristics of Hanning window function and the main lobe fitting technology, this new interpolation method is applicable to all the classical window functions. Besides, the new three-line interpolation method has stronger fault tolerance ability(interpolation direction error) and higher stability under noisy condition.Moreover, the analytic expressions of the interference caused by the image component are derived, and its influences on the traditional 2-point interpolated DFT algorithms are quantitatively analyzed. The phase independences of the radios of both the real parts and the imaginary parts of the complex spectrum line in 2-point interpolated DFT algorithms are proved. Based on the achieved expressions, a novel frequency estimator with high image component interference rejection is proposed, in which the error caused by the image component can be significantly reduced, compared with the traditional algorithms.Finally, the proposed methods are applied to the accurate identification of natural frequency. The results show that the new methods can improve the identification accuracy of natural frequency and have a better anti-disturbance performance.