Abstract: A method comprising collecting magnetic resonance imaging (MRI) scanner data corresponding to a region of interest, establishing a spectral peak profile associated with at least one metabolite in the region of interest, wherein the spectral peak profile comprises a term in the FID vector signal included in the collected MRI scanner data, selecting at least three counter indices and corresponding points on the spectral peak profile to compute a linear fractional transformation (LFT), computing an N-dimensional vector outlining a spectral circle in a complex plane by applying the LFT to each counter index included in a set of equally-spaced counter indices associated with a three-dimensional spectrum representation of the collected MRI scanner data, shifting the spectral circle to eliminate a baseline offset for a magnitude spectrum associated with the complex plane, rotating the shifted spectral circle to produce a rotated spectral circle.

Abstract: A method comprising collecting magnetic resonance imaging (MRI) scanner data corresponding to a region of interest, establishing a spectral peak profile associated with at least one metabolite in the region of interest, wherein the spectral peak profile comprises a term in the FID vector signal included in the collected MRI scanner data, selecting at least three counter indices and corresponding points on the spectral peak profile to compute a linear fractional transformation (LFT), computing an N-dimensional vector outlining a spectral circle in a complex plane by applying the LFT to each counter index included in a set of equally-spaced counter indices associated with a three-dimensional spectrum representation of the collected MRI scanner data, shifting the spectral circle to eliminate a baseline offset for a magnitude spectrum associated with the complex plane, rotating the shifted spectral circle to produce a rotated spectral circle.

Abstract: The present invention generally relates to a method for computing a Fast Fourier Transform (FFT). In one embodiment, the present invention relates to an interleaved method for computing a Fast Fourier Transform (FFT).

Abstract: The present invention generally relates to a method for computing a Fast Fourier Transform (FFT). In one embodiment, the present invention relates to an interleaved method for computing a Fast Fourier Transform (FFT).

Abstract: A method for computing a fast Fourier transform (FFT) in a parallel processing structure uses an interleaved computation process. In particular, the interleaved FFT computation process intertwines the output of two different shifted Fourier matrices to obtain a Fourier transform of an input vector. Next, an even-odd extension process is applied to the transformed input vector, whereupon various terms are grouped in a computational tree. As such, the resulting segmentation of the computation allows the fast Fourier transform to be computed in a parallel manner.

Abstract: General diagnostic and real-time application of digital Hermite functions allows features to be extracted from a measured signal through expansion of the measured signal. Specifically, the digital Hermite functions represent the shape of the measured signal in a set of vectors derived from a symmetrical tridiagonal matrix. This allows for efficient computation of the Hermite expansion coefficients, in real-time, to represent the expanded signal. The signal expansion also allows any artifacts, such as noise, to be isolated and removed, allowing the underlying signal of interest to be revealed.

Abstract: The present invention generally relates to a method for computing a Fast Fourier Transform (FFT). In one embodiment, the present invention relates to an interleaved method for computing a Fast Fourier Transform (FFT).

Abstract: The present invention relates to general diagnostic and real-time applications of discrete Hermite functions to digital data. More specifically, the invention relates to methods and systems for the application of dilated discrete digital Hermite functions (DDHF) to biomedical data, for example, to extract features from digital signals, including but not limited to, ECGs, EMGs, EOGs, EEGs, and others, by expanding the measured signals using a computationally efficient technique. These digital Hermite functions form the basis for the new discrete Hermite transform, generated on a beat by beat basis, which provides information about the shape of the signals, such as that in the BCG artifact in an EEG or in an ECG interval, or any noise in any other electrical signal. An automated system and method for real-time interpretation of any abnormalities present in a digital biomedical signal is provided.

Abstract: A system and method for determining a predicted value of a function from at least one previous value of said function and at least one second-derivative value of the function. The system includes a sensor provided to sense a second-derivative value of the function and transmit an oscillatory signal representing the sensed second-derivative value, a computer-readable memory in communication with the sensor to store the previous value of the function and the second-derivative value, and a feature for computing the predicted value of the function using an integration algorithm including a coefficient of integration that is dependant upon at least a frequency of the signal.

Abstract: A system and method for determining a predicted value of a function from at least one previous value of said function and at least one second-derivative value of the function. The system includes a sensor provided to sense a second-derivative value of the function and transmit an oscillatory signal representing the sensed second-derivative value, a computer-readable memory in communication with the sensor to store the previous value of the function and the second-derivative value, and a feature for computing the predicted value of the function using an integration algorithm including a coefficient of integration that is dependant upon at least a frequency of the signal.

Abstract: A system and method for calculating a future function value, such as velocity, for an object, from derivative values, such as acceleration, includes a sensor, such as an accelerometer, coupled to an object, such as a car. By predetermining a sampling rate of the derivative values and determining the highest frequency in the sampled signal, a set of prediction coefficients can be derived for use in a prediction formula which generates the future function value. A processor, which derives the prediction coefficients and implements the prediction formula may use the future function value to control operation of the object or a related object. By including a past function value in the prediction formula, a highly accurate future function value can be determined.