| Paper: | SPTM-P2.2 | ||
| Session: | Sampling, Extrapolation, and Interpolation | ||
| Time: | Tuesday, May 18, 15:30 - 17:30 | ||
| Presentation: | Poster | ||
| Topic: | Signal Processing Theory and Methods: Sampling, Extrapolation, and Interpolation | ||
| Title: | A GEOMETRICAL APPROACH TO SAMPLING SIGNALS WITH FINITE RATE OF INNOVATION | ||
| Authors: | Yue Lu; University of Illinois at Urbana-Champaign | ||
| Minh N. Do; University of Illinois at Urbana-Champaign | |||
| Abstract: | Many signals of interest can be characterized by a finite numberof parameters per unit of time. Instead of spanning a singlelinear space, these signals often lie on a union of spaces. Underthis setting, traditional sampling schemes are either inapplicable or very inefficient. We present a framework for sampling these signals based on an injective projection operator, which ``flattens'' the signals down to a common low dimensionalrepresentation space while still preserves all the information.Standard sampling procedures can then be applied on that space. We show the necessary and sufficient conditions for such operators to exist and provide the minimum sampling rate for the representation space, which indicates the efficiency of this framework. These results provide a new perspective on the sampling of signals with finite rate of innovation and can serve as a guideline for designing new algorithms for a class of problems in signal processing and communications. | ||
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