Compressed Sampling Methods Of Sparse Signals Based On Shift-invariant Spaces In The Frfd

The sparse signals are composed by a relatively small number of narrowband transmissions across a wide spectrum range in the fractional Fourier domain.These signals are widely applied in the radar whose signals are modulated by the linear modulated frequency signals.According to the extension of Nyquist in the Fr FD,the sampling rates for sparse signals in the Fr FD are as twice as the maximum frequency of the signals.The high frequency of signals leads to the high sampling rate which is difficult to put into practice.The sampling rate is one of the bottleneck of the development of the information system.Compressed sensing(CS)broke up the traditional way of the information acquisition.The classic CS is used to sample the discrete information,which can not be used to deal with the analog signals before the discretization.The traditional analog-to-information conversions(AICs)are available for the sparse signal in the frequency domain,which shows low recovery probability when sampling the sparse signals in the Fr FD.Signals which show better sparsity are widely applied in different situation such as the communication systems.It is important to make the research about the new compressed sampling methods for the sparse signal in the Fr FD and extension of AICs.The main contents and research contributions of this dissertation are as follows:1.Considering the majority of existing sampling models based on shift-invariant(SI)spaces in the Fr FD are constructed by a single generator,which are unable to sample some mixed signals.A theory of generalized SI and sampling spaces associated with the Fr FT is proposed to resolve this problem.The condition and related proof for forming a Riesz basis by the proposed theory are provided.Based on the proposed theory,the non-ideal sampling frameworks which are constructed by a single generator and multiple generators are proposed.Furthermore,the simplified non-ideal sampling models are also shown in the dissertation.Finally,numerical results and several potential applications are presented.2.Considering there are some redundant resources for the non-ideal sampling in generalized SI and sampling spaces.A compressed sampling method was proposed for analog sparse signals in the SI spaces associated the Fr FT.The signals which are belong to the spaces constructed by L functions can be represented by K(K < L)generators,the signals could be sparse when the sparse basis are the generators belong to the SI spaces.Firstly,a compressed sampling method for the sparse signal in the Fr FD is proposed by reusing the sparse basis of the SI spaces.The proposed method combined the sensing matrix of classic compressed sensing and the framework of sampling scheme in the SI spaces to construct a compressed sampling method,which perfectly recovered the original signal with sufficiently low sampling rate.By choosing different filter band,the proposed framework allows to derive many specific sampling schemes.As an example,the random demodulator was redesigned to sample discrete sparse signal in the Fr FD.The mixing vector constructed by random phase sequence has been shown satisfying the incoherent condition.The reconstruction of the representation is based on the orthogonal matching pursuit.The performance of the proposed sampling method is verified by the probability of the successful reconstruction and the mean squared error.3.Considering the traditional analog-to-information system may be difficult to sample signals which show more spare in the Fr FD than in the FD.A multichannel compressed sampling scheme is proposed based on the modulated wideband converter and the Fr FT.The system consists of modulators,analog filters,and analog-to-digital converters.The analog signal is multiplied by a chirp signal and a bank of periodic waveforms.After filtering,the product is uniformly sampled at a rate that is considerably lower than the Nyquist rate.The proposed method which is valid for fractional multiband signals is proven based on the fractional Fourier series.The proposed method would be reduced to be classic MWC when the angle is ?/2.The robustness,recovery accuracy and influence of the fractional order are analyzed by the empirical probability of the successful recovery and the mean squared error.