Abstract: Methods, apparatuses, and systems for calculating time delays by a Wasserstein approach are provided. A plurality of signals are recorded by a plurality of sensors (three or more), respectively, and received at a controller. The plurality of signals recorded by the plurality of sensors are generated in response to a signal emitted by a source. The plurality of signals are converted into a plurality of probability density functions. A cumulative distribution transform for each of the plurality of probability density functions is calculated. A time delay for each unique pair of the plurality of sensors is calculated by minimizing a Wasserstein distance between two cumulative distribution transforms corresponding to the unique pair of the plurality of sensors.

Abstract: Methods, apparatuses, and systems for removing noise from a received signal. A signal is received, at a controller, that was recorded by a sensor and emitted by a source. The signal includes a signal of interest component and a noise component. The noise component of the signal is sampled, and the sampled noise component of the signal is used to estimate a variance in the noise component. An energy of the signal of interest component of the signal is determined. A cumulative distribution function for the received signal is calculated, and a cumulative distribution function of the signal of interest component of the received signal is then calculated based on the estimated variance in the sampled noise component, the determined energy of the signal of interest component of the signal, and the calculated cumulative distribution function for the received signal.

Abstract: Methods, apparatuses, and systems for calculating time delays by a Wasserstein approach are provided. A plurality of signals are recorded by a plurality of sensors (three or more), respectively, and received at a controller. The plurality of signals recorded by the plurality of sensors are generated in response to a signal emitted by a source. The plurality of signals are converted into a plurality of probability density functions. A cumulative distribution transform for each of the plurality of probability density functions is calculated.

Abstract: A photonic compressive sampling system includes a photonic link with at least one electro-optic modulator that modulates a continuous wave optical energy with both an electrical analog signal and a pseudorandom bit sequence signal. A photodetector receives the modulated optical energy from the electro-optic modulator, and an electrical digitizer digitizes the output from the photodetector. The system enables signal recovery beyond the Nyquist limit of the digitizer. The signal being recovered has a sparse (low-dimensional) representation and the digitized samples are incoherent with this representation. An all-photonic system can faithfully recover a 1 GHz harmonic signal even when digitizing at 500 MS/s, well below the Nyquist rate.

Abstract: A photonic compressive sampling system includes a photonic link with at least one electro-optic modulator that modulates a continuous wave optical energy with both an electrical analog signal and a pseudorandom bit sequence signal. A photodetector receives the modulated optical energy from the electro-optic modulator, and an electrical digitizer digitizes the output from the photodetector. The system enables signal recovery beyond the Nyquist limit of the digitizer. The signal being recovered has a sparse (low-dimensional) representation and the digitized samples are incoherent with this representation. An all-photonic system can faithfully recover a 1 GHz harmonic signal even when digitizing at 500 MS/s, well below the Nyquist rate.

Abstract: A system and method for encoding zero and one bits for transmission, including generating a first signal from a non-linear chaotic system to represent the one bit, with the signal's embedded vectors being within the non-linear system's attractor set, and generating a second signal from the non-linear system to represent the zero bit, with the signal's embedded vectors being outside the non-linear system's attractor set. The second signal encoding the zero bit can be generated by adding together two chaotic signals arising from the non-linear system initialized with different initial conditions, and weighting the second signal to have approximately the same energy as the first signal. One suitable chaotic systems is a Lorenz system. Systems and methods for decoding a transmitted stream of signals compare a detection statistic of the received stream of signals to a threshold value that depends on the chaotic system.