Communications and Signal Processing Seminar
Xampling Signal Acquisition and Processing in Union of Subspaces
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Signal processing methods have changed substantially over the last several decades. The number of operations that are shifted from analog to digital is constantly increasing. While technology advances enable mass processing of huge data streams, the acquisition capabilities do not scale sufficiently fast so that the conversion to digital has become a serious bottleneck. For some applications, the maximal frequency of the input signals, which dictates the Nyquist rate, already exceeds the possible rates achievable with existing devices.
In this talk, we present a new framework for sampling and processing wideband analog signals at rates far below that dictated by the Nyquist rate. We refer to this methodology as Xampling: A combination of compression and sampling, performed simultaneously. Xampling merges results from standard sampling theory with recent developments in the field of compressed sensing in order to directly sample a wide class of analog signals at very low rates using existing hardware devices. This paradigm relies on exploiting structure inherent to many different classes of signals, which can be modeled mathematically as a union of subspaces.
We begin by introducing the Xampling methodology and explaining why both sampling and compressed sensing alone are insufficient to address low rate sampling of a wide variety of analog signals. We then consider some specific examples including low rate sampling of multiband signals, recovery of time delays from low rate samples, and more generally sampling and recovery over finite and infinite structured unions of subspaces. We will also discuss circuit considerations in the design of Xampling systems.