Abstract: A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.

Abstract: A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.

Abstract: An improved system and method for communicating information on a transmission medium is disclosed. The disclosed system and method provide improved communications on the transmission medium in the presence of interference, which may take the form of uncorrelated interference from different services on neighboring transmission mediums. In one embodiment, the communications system includes a subscriber modem, a central office modem; and a communications channel coupled between the subscriber modem and the central office modem. The communications channel transports uplink signals from the subscriber modem to the central office modem, and downlink signals from the central office modem to the subscriber modem.

Abstract: System and methods for determining an optimized transmit spectra (spectral distributions of transmission power) for a set of communications channels that experience cross-talk among themselves and for transmitting data on the channels. The transmit spectra are preferably constructed so that largely contiguous frequency bands are allocated to each signaling direction (upstream/downstream) on each communications channel and/or to each channel in the set of channels. In one embodiment, each communications channel is restricted to a maximum time-averaged power. The method preferably includes steps of determining the channel transfer functions of the communications channel, determining interference characteristics of the channels, calculating substantially optimal transmit spectra for the communications channels, and redistributing the frequency bins so that they are contiguously grouped in each transmit spectra. The contiguous groupings allow wider frequency bands for signaling in the channel.

Abstract: A communications system is disclosed having an improved receiver designed to combat ICI in OFDM modulated signals. The receiver may also be designed to combat ISI in OFDM modulated signals. In one embodiment, the communications system comprises a transmitter that transmits an OFDM modulated signal, and a receiver that receives and demodulates a corrupted version of the OFDM modulated signal. The receiver includes an A/D converter, a transform module, and a detection module. The A/D converter converts the corrupted OFDM-modulated signal into a digital receive signal. The transform module transforms the digital receive signal into the frequency domain. The detection module determines a channel symbol from the frequency component amplitudes while compensating for correlation between the frequency components. In a preferred implementation, the detection module calculates for each frequency component, a weighted sum of the frequency component amplitudes from the transform module.

Abstract: A system and method for determining transmission characteristics for a communications channel and for transmitting data on the communications channel. In one embodiment, the method starts by determining the channel's transfer function and determining interference characteristics for the channel. The interference characteristics preferably include transfer functions describing the channel's susceptibility to cross talk from neighboring channels. The channel transfer function and the interference characteristics are then examined and a transmit spectrum (or power spectral density function) is constructed for the channel. The transmit spectrum preferably uses orthogonal separation of upstream and downstream communications to increase channel capacity.

Abstract: A system and method for determining transmission characteristics for a communications channel and for transmitting data on the communications channel. In one embodiment, the method starts by determining the channel's transfer function and determining interference characteristics for the channel. The interference characteristics preferably include transfer functions describing the channel's susceptibility to cross talk from neighboring channels. The channel transfer function and the interference characteristics are then examined and a transmit spectrum (or power spectral density function) is constructed for the channel. The transmit spectrum preferably uses orthogonal separation of upstream and downstream communications to increase channel capacity.