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Tuesday, February 12, 2013

Analog to Information: Breaking the Nyquist barrier


I recently stumbled on a site set up by Emmanuel Candes featuring some of the Analog to Information (A2I) work (and associated hardware). Here is an extract of the first page:( there is also a page on the Random Modulator Pre-Integrator, the Non-Uniform Samplerthe whole team is here and all the papers under that effort are here)

"....A new type of mathematics for signal processing
Something scenic
Beginning in 2004, a new mathematical theory called "compressed sensing" (CS) has turned conventional signal processing upside-down. CS has applications outside of signal processing, but this project focuses on just applying it to analog-to-digital converters (ADC). Conventional ADC sample analog signals at twice the bandwidth contained in the signal, according to the Nyquist sampling theorem that is taught in freshman electrical engineering courses. The drawback of this approach is that the bandwidth of a signal may be a poor proxy for how much information is in the signal, and so ADC sample at unnecessarily high rates. Unfortunately, high-rate sampling is inherently more difficult than low-rate sampling. The approach of compressed sensing is to change how we sample, and the benefit is that it is now possible to sample at the information-rate, which can lead to sampling at rates that are orders of magnitude slower than the Nyquist rate.
There are three things that make CS possible. The first is a new type of sampling scheme, which is that the A2I project is about. The second is powerful modern mathematics to provide conditions when the approach works, and the third item is efficient algorithms to convert the samples back to the original signal. More information on the mathematics and algorithms can be found in the references contained on this website.,,,"
I like their mention of Nuit Blanche


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