Optimized sampling and processing of structured signals

• Applicant: Dr.-Ing. Ullrich Mönich
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2012 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 229268497

Today's information society is based on the power of digital signal processing, and the theoretical foundation for the digital processing of analog signals is the Shannon sampling theorem. Without any further information about bandlimited signals, Nyquist rate sampling is essentially optimal. However, if the signals have some additional structure-as is the case in many applications-it is possible to reduce the sampling rate below the Nyquist rate. The new field of compressed sensing provides a framework for sampling and recovering of sparse signals. However, sparsity is only one of many possible structures a signal can have. A specialized signal processing, including sampling, digital processing and subsequent reconstruction, that is adapted to the signal structure will lead to a post-Shannon sampling theory. Currently, it is not fully understood whether the new theory can replace the current standard theory, which has proven very useful but also shown to fail in several important cases, or if the new theory is an extension of the old one, so that the two theories complement each other. The goal of this project is to study the theoretical foundations of an adapted sampling, processing, and reconstruction for signals that have a specific structure. To this end, suitable signal spaces will be identified and new algorithms will be developed. The ideas of compressed sensing will be applied to more general signal classes, in particular to sparse analog signals, and used to develop new methods for system approximation. Further, practical applications and the influence of impairments like quantization and noise will be examined.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Vivek Goyal