Abstract: A system, method, and memory medium for operating on an electrocardiogram (ECG) signal. A multiscale short-time Fourier transform (STFT) is perform on a set of ECG samples {s(n)} to obtain a transform array. For each sufficiently energetic peak in the transform array, a refined window width value and a refined window displacement value is generated by: computing an inner product between the set of samples and each of a plurality of functions, where the plurality of functions are sufficiently close to a coarse approximation function given by the peak location; and solving a linear system Av=c for the unknown vector v, where the vector c is determined by the inner products, where the matrix A is determined by the center times of the plurality of functions. After appropriate selection, the refined window width and refined window displacement may be used to represent ECG waveform features.

Abstract: A system, method, and memory medium for operating on an electrocardiogram (ECG) signal. A multiscale short-time Fourier transform (STFT) is perform on a set of ECG samples {s(n)} to obtain a transform array. For each sufficiently energetic peak in the transform array, a refined window width value and a refined window displacement value is generated by: computing an inner product between the set of samples and each of a plurality of functions, where the plurality of functions are sufficiently close to a coarse approximation function given by the peak location; and solving a linear system Av=c for the unknown vector v, where the vector c is determined by the inner products, where the matrix A is determined by the center times of the plurality of functions. After appropriate selection, the refined window width and refined window displacement may be used to represent ECG waveform features.

Abstract: A system, method and memory medium for operating on an electrocardiogram (ECG) signal. A multiscale short-time Fourier transform (STFT) is performed on a set of ECG samples {s(n)} to obtain a transform array. For each sufficiently energetic peak in the transform array, a refined window width value and a refined window displacement value is generated by: computing an inner product between the set of samples and each of a plurality of functions, where the plurality of functions are sufficiently close to a coarse approximation function given by the peak location; and solving a linear system Av=c for the unknown vector v, where the vector c is determined by the inner products, where the matrix A is determined by the center times of the plurality of functions. After appropriate selection, the refined window width and refined window displacement may be used to represent ECG waveform features.

Abstract: A system, method and memory medium for operating on an electrocardiogram (ECG) signal. A multiscale short-time Fourier transform (STFT) is perform on a set of ECG samples {s(n)} to obtain a transform array. For each sufficiently energetic peak in the transform array, a refined window width value and a refined window displacement value is generated by: computing an inner product between the set of samples and each of a plurality of functions, where the plurality of functions are sufficiently close to a coarse approximation function given by the peak location; and solving a linear system Av=c for the unknown vector v, where the vector c is determined by the inner products, where the matrix A is determined by the center times of the plurality of functions. After appropriate selection, the refined window width and refined window displacement may be used to represent ECG waveform features.

Abstract: System and method for performing Time Domain Reflectometry (TDR) on a Device Under Test (DUT) using Gaussian pulses. A signal is received comprising an initial Gaussian pulse and one or more reflected pulses from the DUT. Each pulse is characterized by determining a set of estimated parameters, permuting the estimated parameter set to generate one or more permuted parameter sets, generating linear equations from the parameter sets, including parameter variables for the corresponding Gaussian pulse, and determining values for the parameter variables by solving the linear equations. The determined parameters characterize the Gaussian pulse. If there are N parameters to determine and M permutations generated, where M is greater than or equal to N, M+1 linear equations are solved to overdetermine the N parameters. The determined parameters of the initial pulse and the one or more reflected pulses are useable to perform TDR analysis on the DUT.

Abstract: A system and method for analyzing order components present in a physical signal X acquired from a physical system. Measurement information for the physical signal X may be received, where the measurement information includes information indicating a plurality of order components of the physical signal X. Time frequency plot information visually indicating order components of the physical signal X may be displayed. User input selecting one or more of the visually indicated order components may be received. A time domain signal may be created based on the one or more selected order components and may then be presented to a user on a presentation device. Presenting the time domain signal on the presentation device may enable the user to analyze the physical signal X or the physical system. Where the physical system includes one or more rotating elements, the method may enable order components of the signal to be analyzed even when no rotation speed information (e.g.

Abstract: System and method for characterizing a Gaussian pulse in a signal. The system includes a computer operable to receive the signal, determine a set of estimated parameters for the Gaussian pulse using a “zoom-in” approach, permute the estimated parameter set to generate one or more permuted parameter sets, where the estimated and permuted parameter sets each represent a corresponding waveform, generate closed form inner products between the received signal and each waveform, generate linear equations from the inner products, each linear equation being a function of a respective one of the parameter sets and corresponding parameter variables for the Gaussian pulse, and determine values for the parameter variables by solving the linear equations. The determined parameters characterize the Gaussian pulse. If there are N parameters to determine and M permutations generated, where M is greater than or equal to N, M+1 linear equations are solved to overdetermine the N parameters.

Abstract: System and method for performing Time Domain Reflectometry (TDR) on a Device Under Test (DUT) using Gaussian pulses. A signal is received comprising an initial Gaussian pulse and one or more reflected pulses from the DUT. Each pulse is characterized by determining a set of estimated parameters, permuting the estimated parameter set to generate one or more permuted parameter sets, generating linear equations from the parameter sets, including parameter variables for the corresponding Gaussian pulse, and determining values for the parameter variables by solving the linear equations. The determined parameters characterize the Gaussian pulse. If there are N parameters to determine and M permutations generated, where M is greater than or equal to N, M+1 linear equations are solved to overdetermine the N parameters. The determined parameters of the initial pulse and the one or more reflected pulses are useable to perform TDR analysis on the DUT.

Abstract: A system and method for analyzing order components present in a physical signal X acquired from a physical system. Measurement information for the physical signal X may be received, where the measurement information includes information indicating a plurality of order components of the physical signal X. Time frequency plot information visually indicating order components of the physical signal X may be displayed. User input selecting one or more of the visually indicated order components may be received. A time domain signal may be created based on the one or more selected order components and may then be presented to a user on a presentation device. Presenting the time domain signal on the presentation device may enable the user to analyze the physical signal X or the physical system. Where the physical system includes one or more rotating elements, the method may enable order components of the signal to be analyzed even when no rotation speed information (e.g.

Abstract: System and method for characterizing a Gaussian pulse in a signal. The system includes a computer operable to receive the signal, determine a set of estimated parameters for the Gaussian pulse using a “zoom-in” approach, permute the estimated parameter set to generate one or more permuted parameter sets, where the estimated and permuted parameter sets each represent a corresponding waveform, generate closed form inner products between the received signal and each waveform, generate linear equations from the inner products, each linear equation being a function of a respective one of the parameter sets and corresponding parameter variables for the Gaussian pulse, and determine values for the parameter variables by solving the linear equations. The determined parameters characterize the Gaussian pulse. If there are N parameters to determine and M permutations generated, where M is greater than or equal to N, M+1 linear equations are solved to overdetermine the N parameters.