Abstract: A data processing technique includes: accessing a matrix (M) representing a graph; wherein: the graph comprises a plurality of nodes to be clustered and a plurality of edges; an edge in the plurality of edges represents an association between two of the plurality of nodes; and an entry of the matrix has a corresponding edge among the plurality of edges. The technique further includes performing an operation on the matrix to generate a result matrix, the operation includes a multiplication function on the matrix; and identifying one or more clusters among the plurality of nodes, based at least in part on the result matrix, including detecting one or more vertices among the plurality of nodes using the result matrix.

Abstract: Matrix processing includes: initializing a current matrix based at least in part on an original matrix; iteratively determining a matrix property using a plurality of iteration cycles, including, in an iteration cycle: partitioning the current matrix to obtain a plurality of partitions, wherein the plurality of partitions includes a submatrix; modifying the submatrix based at least in part on other partitions of the plurality of partitions to provide a current matrix for a next iteration; and continuing to iterate until a condition is met. Matrix processing further includes obtaining the matrix property from an iteration result; and outputting the matrix property.

Abstract: Tensor analysis includes: obtaining a set of Fourier domain singular value decomposition (SVD) factors of a first tensor representing data in multiple dimensions, including: performing Fourier transform on the first tensor along a first dimension to obtain a Fourier domain tensor; performing SVD on the Fourier domain tensor to obtain a first set of Fourier domain SVD tensors; performing inverse Fourier transform on at least some of the first set of Fourier domain SVD tensors to obtain a set of native domain tensors; performing Fourier transform on at least some of the set of native domain tensors to obtain a second set of Fourier domain tensors; performing SVD on at least some of the second set of Fourier domain tensors to obtain a second set of Fourier domain SVD tensors; obtaining an SVD result based at least in part on the set of Fourier domain SVD factors of the first tensor; and outputting at least a portion of the SVD result.

Abstract: A data processing technique includes: accessing a matrix (M) representing a graph; wherein: the graph comprises a plurality of nodes to be clustered and a plurality of edges; an edge in the plurality of edges represents an association between two of the plurality of nodes; and an entry of the matrix has a corresponding edge among the plurality of edges. The technique further includes performing an operation on the matrix to generate a result matrix, the operation includes a multiplication function on the matrix; and identifying one or more clusters among the plurality of nodes, based at least in part on the result matrix, including detecting one or more vertices among the plurality of nodes using the result matrix.

Abstract: Matrix processing includes: accessing an original matrix; iteratively determining a plurality of estimated singular vectors of the original matrix, a plurality of estimated singular values of the original matrix, or both, using a plurality of iteration cycles; wherein at least some of the plurality of iteration cycles are performed in parallel on a plurality of processors; and outputting the plurality of estimated singular vectors of the original matrix, the plurality of estimated singular values of the original matrix, or both.

Abstract: A tensor processing technique includes: accessing a first tensor representing interconnections of a plurality of nodes, the first tensor being a tensor of three or more dimensions; accessing a second tensor; convolving the first tensor with the second tensor to generate a convolution result tensor; and outputting at least a portion of the convolution result tensor.

Abstract: A tensor processing technique includes: accessing a tensor, wherein the tensor: represents interconnections of nodes across one or more dimensions, comprises a plurality of matrices, and forms a plurality of vectors across at least one of the one or more dimensions; applying Fourier Transform on the tensor to obtain a plurality of harmonic matrices; performing singular value decompositions (SVDs) on the plurality of harmonic matrices to obtain a plurality of corresponding SVD results; reducing the plurality of corresponding SVD results, including selecting one or more dominant components in the plurality of corresponding SVD results to obtain one or more reduced results; and performing Inverse Fourier Transform on the one or more reduced results to obtain a de-noised tensor.

Abstract: Matrix processing includes: initializing a current matrix based at least in part on an original matrix; iteratively determining a matrix property using a plurality of iteration cycles, including, in an iteration cycle: partitioning the current matrix to obtain a plurality of partitions, wherein the plurality of partitions includes a submatrix; modifying the submatrix based at least in part on other partitions of the plurality of partitions to provide a current matrix for a next iteration; and continuing to iterate until a condition is met. Matrix processing further includes obtaining the matrix property from an iteration result; and outputting the matrix property.

Abstract: A data processing technique includes: accessing a matrix (M) representing a graph; wherein: the graph comprises a plurality of nodes to be clustered and a plurality of edges; an edge in the plurality of edges represents an association between two of the plurality of nodes; and an entry of the matrix has a corresponding edge among the plurality of edges. The technique further includes performing an operation on the matrix to generate a result matrix, the operation includes a multiplication function on the matrix; and identifying one or more clusters among the plurality of nodes, based at least in part on the result matrix, including detecting one or more vertices among the plurality of nodes using the result matrix.

Abstract: Matrix processing includes: initializing a current matrix based at least in part on an original matrix; iteratively determining a matrix property using a plurality of iteration cycles, including, in an iteration cycle: partitioning the current matrix to obtain a plurality of partitions, wherein the plurality of partitions includes a submatrix; modifying the submatrix based at least in part on other partitions of the plurality of partitions to provide a current matrix for a next iteration; and continuing to iterate until a condition is met. Matrix processing further includes obtaining the matrix property from an iteration result; and outputting the matrix property.

Abstract: A distortion correcting analog to digital converter (ADC) system includes a plurality of ADCs configured to convert an analog signal to a plurality of digital ADC outputs, wherein the plurality of ADCs are configured to generate a composite signal based on the plurality of ADC outputs, there is an offset between a first one of the plurality of ADC outputs and a second one of the plurality of ADC outputs, and the offset causing distortion in the composite signal. The distortion correcting ADC system further includes an adaptive module coupled to the plurality of ADCs, wherein the adaptive modules includes an adaptive filter having a filter response, and the adaptive module is configured to adaptively adjust the filter response to reduce the distortion in the composite signal.

Abstract: A method of signal processing includes receiving an unknown signal that includes a distorted component and an undistorted component, and performing self-linearization based at least in part on the unknown signal to obtain an output signal that is substantially undistorted, wherein performing self-linearization includes adaptively generating a replica distortion signal that is substantially similar to the distorted component, and subtracting the replica distortion signal from the unknown signal to obtain the output signal.

Abstract: A signal processing method includes receiving a digital signal includes a plurality of samples associated with a plurality of original sampling times, wherein the original sampling times have a period of T; generating, based on the digital signal, a nominal phase shifted signal having a plurality of nominal phase shifted samples associated with a plurality of phase shifted sampling times, wherein the plurality of phase shifted sampling times correspond to fractional intervals of the original sampling times; and generating a compensated signal based at least in part on the digital signal and the nominal phase shifted signal. A signal processing system includes a receiving terminal configured to receive a digital signal comprising a plurality of samples associated with a plurality of original sampling times, wherein the original sampling times have a period of T, and a compensation module coupled to the receiving terminal.

Abstract: A method of converting an input analog signal to a compensated digital signal comprises converting the input analog signal to an uncompensated digital signal, inputting the uncompensated digital signal to a distortion model, generating a modeled distortion signal based on the uncompensated digital signal, and subtracting the modeled distortion signal from the uncompensated digital signal to generate the compensated digital signal. A distortion compensating analog to digital converter (ADC) comprises an uncompensated ADC configured to convert an input analog signal to an uncompensated digital signal, and a compensation module coupled to the uncompensated ADC, configured to receive the uncompensated digital signal, generate a modeled distortion signal based on the uncompensated digital signal and subtract the modeled distortion signal from the uncompensated digital signal to generate the compensated digital signal.

Abstract: An observation system configured to observe at least one known state variable of an observed system includes a plurality of filters that are configured to receive a system input, and generate the at least one unknown state variable. Generating the unknown state variable includes processing the system input, a plurality of known state variables, and a time varying mode vector. An inverse system configured to observe at least one inverse state variable of an original system includes a plurality of filters that are configured to receive a system input, and generate the at least one inverse state variable. Generating the inverse state variable includes processing the system input, a plurality of known state variables associated with the original system, and a time varying mode vector associated with the original system.

Abstract: A system and method are disclosed for processing a signal propagated through a nonlinear channel. The method includes modeling the channel characteristics to produce a linearized channel model, deriving an inverse linearized channel model from the linearized channel model, and filtering the signal using the inverse linearized channel model.

Abstract: A system and method are disclosed for correcting for output distortion of an analog to digital converter, comprising: estimating the output distortion, providing an estimated distortion, and combining an output of the analog to digital converter with the estimated distortion to compensate for the output distortion. The compensating module for correcting output distortion of an analog to digital converter comprises a calibration module configured to estimate the output distortion and a combiner configured to combine an output of the analog to digital converter with the estimated distortion to compensate the output distortion.

Abstract: A method of compensating for nonlinear distortions in a digital signal comprises receiving the digital signal, generating a nominal phase shifted signal based on the digital signal, generating a modeled distortion signal based on the digital signal and the nominal phase shifted signal, subtracting the modeled distortion signal from the digital signal, and generating a compensated signal. A compensating system comprises an input interface configured to receive a digital signal having nonlinear distortion, and a distortion model coupled to the interface, configured to generate a nominal phase shifted signal based on the digital signal, generate a modeled distortion signal based on the digital signal and the nominal phase shifted signal, subtract the modeled distortion signal from the digital signal, and generate a compensated signal.

Abstract: A method of converting an input analog signal to a compensated digital signal comprises converting the input analog signal to an uncompensated digital signal, inputting the uncompensated digital signal to a distortion model, generating a modeled distortion signal based on the uncompensated digital signal, and subtracting the modeled distortion signal from the uncompensated digital signal to generate the compensated digital signal. A distortion compensating analog to digital converter (ADC) comprises an uncompensated ADC configured to convert an input analog signal to an uncompensated digital signal, and a compensation module coupled to the uncompensated ADC, configured to receive the uncompensated digital signal, generate a modeled distortion signal based on the uncompensated digital signal and subtract the modeled distortion signal from the uncompensated digital signal to generate the compensated digital signal.

Abstract: A method of processing an input signal that includes an input variable is disclosed. The method comprises comparing the input variable to a set of ordered constants, determining the relative location of the input variable within a range of possible inputs and determining a filter coefficient of a nonlinear filter using the relative location of the input variable. A configurable filter comprises an interface configured to receive an input signal that includes an input variable, a nonlinear filter coupled to the interface, configured to process the input signal, and a processor coupled to the nonlinear filter, configured to determine the relative location of the input variable within a range of possible inputs and to determine a filter coefficient of the nonlinear filter using the relative location of the input variable.