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Pittsburgh, PA, United States

Hamschin B.M.,48 Benedum Hall | Loughlin P.J.,49 Benedum Hall
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2011

We extend a recent method by Kay that maximizes the probability of detecting an elastic object in the presence of Gaussian reverberation and additive Gaussian interference. Kay's solution specifies the spectral magnitude for the optimal transmit waveform, and hence there is an unlimited number of "optimal" waveforms that can be transmitted, all with the same spectral magnitude but differing in terms of time domain characteristics such as duration and peak power. We extend Kay's approach in order to obtain a unique optimal waveform by incorporating time-domain constraints, via two optimization problem formulations. One approach yields a waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second complementary approach considers temporal concentration rather than duration, and yields a waveform that, depending on the degree of concentration imposed, achieves the optimal the spectral magnitude to varying degrees. © 2011 SPIE.

Senay S.,48 Benedum Hall | Chaparro L.F.,48 Benedum Hall | Sun M.,48 Benedum Hall | Sun M.,University of Pittsburgh | And 3 more authors.
Turkish Journal of Electrical Engineering and Computer Sciences | Year: 2011

Brain-computer interfaces (BCIs) provide a way to monitor and treat neurological diseases. An important application of BCIs is the monitoring and treatment of epilepsy, a neurological disorder characterized by recurrent unprovoked seizures, symptomatic of abnormal, excessive or synchronous neuronal activity in the brain. BCIs contain an array of sensors that gather and transmit data under the constrains of low-power and minimal data transmission. Asynchronous sigma delta modulators (ASDMs) are considered an alternative to synchronous analog to digital conversion. ASDMs are non-linear feedback systems that enable time-encoding of analog signals, from which the signal can be reconstructed. An efficient reconstruction of time-encoded signals can be achieved using a prolate spheroidal waveform (PSW) projection. PSWs have finite time support and maximum energy concentration within a given bandwidth. The ASDM time-encoding is related to the duty-cycle modulation and demodulation, which shows that sampling is non-uniform. For transmission of data from BCI, we propose a modified orthogonal frequency division multiplexing (OFDM) technique using chirp modulation. Our method generalizes the chirp modulation of binary streams with non-uniform symbol duration. Our theoretical results relate to recent continuous-time digital signal processing and compressive sampling theories. © TÜBİTAK.

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