Continuous Spectrum Analysis In Discrete Spectrum Correction

Continuous spectrum correction in discrete spectrum correction is presented in this thesis. The study is based on the project of National Natural Science Fund of China, the State Ministry of Education of China and State Key Laboratory of Vibration, Shock and Noise, which deeply research on continuous spectrum correction In discrete spectrum correction.Based on an investigation of the amplitude errors in Fourier transform and spectrum analysis produced by windowing, this paper, on the principles of equivalent amplitude and energy, presents three methods to calculate the resetting modulus for windowing spectrum analysis so as to reduce the errors. The first method is by calculating resetting modulus through theoretical deduction directly. The second method is by calculating the energy resetting modulus with numerical integrating. The third method is by calculating the energy resetting modulus emulating computation. The second or the third method is to be used in cases where the function in domain of time of window is too complicated or the spectrum of window is unreachable, with different resetting moduli to be chosen for different methods for use in spectrum correction.A new method of estimating characteristic parameters for continuous spectrum of response signal of damped free vibration is presented in this paper. This signal could be considered as a product of the harmonic wave and the unilateral exponential window and the rectangle window. By FFT and DFT, we estimate the frequency corresponding to the peak and its amplitude and phase. According to the frequency-domain convolution theorem, we can prove the peak frequency and phase are frequency and phase of the harmonic wave signal. By solving the equation of amplitude, we get the correct amplitude. It is a method that can be used to calculate the characteristic parameters with no errors in theory when the coupling among frequencies is not considered. Simulation shows if the signal is not affected by noise, the maximum error of frequency, amplitude and phase respectively is Oand 0.7% and 3.5 degree. When the signal is affected by noise (SNR=7.3), it still has high precision, the maximum error of frequency and amplitude and phase is respectively 0 and 4.7%and 6.5 degree. The variety of estimating precision is analyzed as the variety of sampling frequency, frequency, damping, amplitude and phase. When one frequency is close to the others and the coupling is not very severe, we can enhance the precision by the second correction. If the interval between frequencies is reduced to a certain value, the coupling will be so severe that this method can not be used.