Abstract：According to the sparse signals feature that power is included in only several parts of frequency bands,a model of periodic non-uniform sampling and reconstruction is built in order to effectively sample sparse signals.The sampling and reconstruction of sparse signals are transformed into vector operations by using theory of union of subspaces.Locations of non-zero row vector are identified with the aid of the mode of the multiple measurement vectors,and the complete reconstruction of sparse signal is achieved in virtue of interpolations,which can insure that the signals could be applied in digital system.Finally,simulation and experimentation demonstrated that the model can effectively achieve acquisition and reconstruction of sparse signals.
［1］Baraniuk R.A lecture on compressive sensing［J］.IEEE Signal Processing Magazine,2007,24(4): 118-121.
［2］Candès E J.An introduction to compressive sampling［J］.IEEE Signal Processing Magazine,2008,25(2):21-30.
［3］Meng C,Tuqan J. Generalized periodic non-uniform sampling of non-bandlimited signals［C］// Information Theory and Applications Workshop,San Diego,CA,USA,2008.
［4］Nguyen H T,Do M N. Signal reconstruction from a periodic nonuniform set of samples using H∞ optimization［J］.IEEE Trans Signal Proc,2005,53(5): 1731-1738.
［5］Donoho D.Compressed sensing［J］.IEEE Transactions on Information Theory,2006,52(4): 1289-1306.
［6］Candès E J. Compressive sampling［C］// The International Congress of Mathematicians,Madrid,Spain,2006.
［7］Cotter S F.Sparse solutions to linear inverse problems with multiple measurement vectors［J］.IEEE Transactions on Signal Processing,2005,53(7):2477-2489.
［8］Mishali M.Reduce and boost: recovery arbitrary sets of jointly sparse vectors［J］.IEEE Transactions on Signal Processing,2008,56(10):4692-4701.
［9］LU Y M.A theory for sampling from a union of subspace［J］.IEEE Transactions on Signal Processing,2008,56(6): 2334-2345.
［10］朱肇轩,王厚军,王志刚.并行采样时多带信号重构函数的一种确定方法［J］.计量学报,2009,30(6):559-562.
2012, Vol. 33 
