Research On Sampling And Reconstruction Based On Finite Rate Of Innovation In The Fractional Fourier Domain

Sampling,an important and essential part of digital communication system,is at theheart of analog-to-digital conversion. Nyquist made great contributions to samplingresearch by proposing the famous Nyquist sampling theorem.Since Nyquist,with furtherinvestigation of signal process theory,many new theoretical tools and sampling methodsspring up based on conventional Fourier transform(FT).Among them,fractional Fouriertransform(FRFT) and finite rate of innovation(FRI) theory are quite novel andcompelling.As a generalized form of FT,FRFT is able to analyze and process signals infractional domain between time domain and frequency domain,which breaks thelimitation of FT.FRI theory is mainly used to process signals that Nyquist theory cannotdeal with,such as sparse non-bandlimited signals.It breaks the limitation of Nyquist rateand implements perfect reconstruction by sampling at finite rate of innovation,whichmens a great reduction of sampling rate.Combination of FRFT and FRI will lead tofurther and more flexible study of signal processing theory,such as reconstruction offractional non-bandlimited signals.This dissertation begins by introducing the basic principles of FRFT andFRI,including definitions,basic propertities,basic comprehensions and so on.Based onFRFT and FRI,researchs of typical signals with finite rate of innovation are carried onabout sampling and reconstruction. The attempt of non-uniform sampling in thesampling process is also discussed.Taking noise into account,reconstruction algorithmin the presence of noise is proposed.The anti-noise performance and numerical stabilityare enhanced and the simulation is carried on. Finally,this dissertation discusses thepractical application of the above studies,including multipath channel estimation andanti-pulse interference.According to the special form of impulse response of multipathchannel,FRI theory is one of the optimal choices for multipath channelestimation.Complicated training sequence design is not necessary any more.Throughsampling the received signal in the fractional domain in which the power of thereference signal is the best accumulative,the effect of noise can be significantlyreduced.Then higher estimation accuracy will be obtained while total process has lowcomputational complexity.The framework is presented and numerical experiment is demonstrated to support the theoretical analysis.Impulse interference is one of the mostcommon interferences. In the fractional Fourier domain, the effect of impulse noise iswell eliminated by modeling impulse noise reasonably based on FRI.Theoreticalanalysis is presented and contrast simulation is demonstrated.