Signal Reconstruction Method Based On Generalized Inverse

Sampling and construction theory has long been a hotspot in the field ofwireless communication. With the development of wireless technology, thisenables the modulation of narrow-band signals by high carrier frequencies.To demodulate the desired signals, the required sampling rate for the ADCcould often be too high to be attained if the Nyquist sampling theorem is tobe satisfied. Therefore, the multi-level down-conversions are used beforethe RF or microwave signals are sampled. However, this method increasesthe complexity of the hardware and leads to signal distortion. Recently, thehigh-speed, high-resolution sampling and reconstruction technology growto currently one of the hottest topics in the field of signal sampling andprocessing.The various signals in actual project are the main object of study inthis paper. The periodic non-uniform is used to sample the signals on thebasis of analysis of the characteristics of the various signals in details.Complete reconstruction or partial reconstruction of the signal according to the actual needs by using the generalized inverse.In this paper, the proposed sampling model based on generalizedinverse, reconstruction method, the image frequency suppression is studied.1) From the Shannon theory, according to the feature of periodicnon-uniform sampling that it needs multiple channels，the sampling andreconstruction of signals were transformed into matrix and vectoroperations by using theory of union of subspaces, the constructed signalcan be obtained by using generalized inverse, and the condition whichconstitute the proposed system is studied. The oversampling andsubsampling in shift-invariant space are defined;2) The least square method is used to get the generalized inverse forthe oversampling system in the chapter. The complete reconstruction ofsampled sparse signal is achieved in virtue of interpolations, which caninsure that the signals could be applied in digital system. An adaptativeiterative compensation is employed to compensate the offset of sensingmatrix. The conclusion shows the frame-work presented here is feasible.3) The subsampling construction is proposed for sampling sparsesignals. The define of sparse signals, the determination of sparsity and division of the band is described in detail; The aim of the algorithm such asorthogonal matching pursuit, minimum L1normal, multiple measurementvectors etc. is to find the unique sparse representation of the sampled sparsesignals, which is the set of indices corresponding to the non-zero elements;the complete reconstruction of sparse signal is achieved in virtue ofinterpolations. The necessary condition of reconstruction is analyzed; aback-end feedback adaptative compensation system is proposed;multi-band signals are taken as an example to prove that the method canachieve the sampling and reconstruction of sparse signals.4) A new method of the image frequency suppression based ongeneralized inverse is proposed in this chapter. However, the imageattenuation alone is clearly insufficient for band-pass signals. To enhancethis obtainable image attenuation an interference canceled of compensationstructure is proposed. The conclusion shows the frame-work presented hereis better than the traditional method.