Reservoir Labs, Inc.

Qualcomm Incorporated

Significs and Elements, LLC

Pierre-David Letourneau

Mitchell Harris

A system for determining the frequency coefficients of a one or multi-dimensional signal that is sparse in the frequency domain includes determining the locations of the non-zero frequency coefficients, and then determining values of the coefficients using the determined locations. If N is total number of frequency coefficients across the one or more dimension of the signal, and if R is an upper bound of the number of non-zero ones of these frequency coefficients, the systems requires up to (O(Rlog(R) (N))) samples and has a computation complexity of up to O(Rlog(R) log (N). The system and the processing technique are stable to low-level noise and can exhibit only a small probability of failure. The frequency coefficients can be real and positive or they can be complex numbers.

Systems and method for determining frequency coefficients of signals

A technique for measuring properties of a material includes measuring the electromagnetic radiation scattered by one or more scattering points associated with the material, and adjusting the radiation according to the respective sensitivities of the scattering points to changes in material properties at that scattering point for several pairs of radiation sources and receivers. The material properties are determined using the updated measurements and corresponding simulated measurements.

System and method for electromagnetic beamforming and imaging at low frequency

A system for determining the frequency coefficients of a one or multi-dimensional signal that is sparse in the frequency domain includes determining the locations of the non-zero frequency coefficients, and then determining values of the coefficients using the determined locations. If N is total number of frequency coefficients across the one or more dimension of the signal, and if R is an upper bound of the number of non-zero ones of these frequency coefficients, the systems requires up to (O (R log(R) (N))) samples and has a computation complexity of up to O (R log(R) log (N). The system and the processing technique are stable to low-level noise and can exhibit only a small probability of failure. The frequency coefficients can be real and positive or they can be complex numbers.

A signal pre-compensation system analyzes one or more properties of a communication medium and, taking advantage of the locality of propagation, generates using sparse fast Fourier transform (sFFT) a sparse kernel based on the medium properties. The system models propagation of data signals through the medium as a fixed-point iteration based on the sparse kernel, and determines initial amplitudes for the data symbol(s) to be transmitted using different communication medium modes. Fixed-point iterations are performed using the sparse kernel to iteratively update the initial amplitudes. If the iterations converge, a subset of the finally updated amplitudes is used as launch amplitudes for the data symbol(s). The data symbol(s) can be modulated using these launch amplitudes such that upon propagation of the pre-compensated data symbol(s) through the communication medium, they would resemble the original data symbols at a receiver, despite any distortion and/or cross-mode interference in the communication medium.

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Pierre-David Letourneau