Adaptive Signal Processing

Adaptive frequency band (AFB) and ultra-wideband (UWB) systems require either rapidly changing or very high sampling rates. Conventional analog-to-digital devices are nonadaptive and have limited dynamic range. We investigate AFB and UWB sampling via a basis projection method. The method decomposes the signal into a basis over time segments via a continuous-time inner product operation and then samples the basis coefficients in parallel. The signal may then be reconstructed from the basis coefficients to recover the signal in the time domain. The overarching goal of the theory developed in this chapter is to develop a computable atomic decomposition of time-frequency space. The idea is to come up with a way of nonuniformly tiling time and frequency so that if the signal has a burst of high-frequency information, we tile quickly and efficiently in time and broadly in frequency, whereas if the signal has a relatively low-frequency segment, we can tile broadly in time and efficiently in frequency. Computability is key; systems are designed so that they can be constructed using splines and implemented in circuitry.

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