Research Of Time-frequency Analysis For Chirp Signal Based On Fractional Fourier Transform

Time-frequency analysis is a powerful tool for non-stationary signal processing. AndChirp signal of non-stationary signals is often used as a measure of whether a time-frequencyanalysis method is effective because of its best time-frequency aggregation in thetime-frequency plane distribution. The fractional Fourier transform(FRFT), which is ageneralization of the classical Fourier transform, can be interpreted as a signal in thetime-frequency plane of any angle of fractional Fourier domain after the origincounterclockwise rotation. It can show all changes of signal characteristics gradually fromtime domain to frequency domain. Therefore, this thesis mainly analysis the time-frequencydistribution of Chirp signal based on the FRFT. The main research in this thesis is as follows:1. Study on the basis theoretical of the second-order central moments of FRFT andpromote second-order central moments to kth-order central moments. At the same time, thechoice of the best rotation angle about different value of k is discussed under the condition ofdifferent SNR. Chirp signal would present a pulse signal in the optimal fractional domainafter rotating one of appropriate angle. So the estimation of the best rotation angle is veryimportant. This thesis uses the different order central moments of the FRFT to estimate thebest rotation angle in the case of low SNR after studying the traditional second-order centralmoment of FRFT. Results show that the fourth-order center moment of FRFT have theadvantages far outweigh the other order central moments under the condition of low SNR.2. Study on multi-component Chirp signals separation based on pseudo Wigner-Villerdistribution in short-time fractional Fourier domain. For multi-component Chirp signals,especially its cross each other, time domain, frequency domain and time-frequency domainwill have overlapping part. So multi-component Chirp signal separation is he basis of furtheranalysis on characteristics of each component. First adopted the fourth center moment ofFRFT estimates the best rotation angle. And then, the proposed pseudo Wigner-Ville distributionrealize multi-component Chirp signals separation based on rotated short-time Fourier transform. Simulationresults show the method is effective.3. Study on suppression of cross-term of Wigner-Ville distribution for multi-componentChirp signals adopts S-method in short-time fractional Fourier domain. The method bycombining FRFT and S-method is used to suppress the cross-term of Wigner-Ville distributionin the optimal short-time fractional Fourier domain. The theoretical analysis and simulationresults show the proposed method can effectively suppress cross-term of WVD forintersection and mutually exclusive multi-component Chirp signals in the case of additiveGaussian white noise.