A matrix-based pattern prediction system of the present disclosure is that of a multi-block matrix-based system that operates on an input signal having a time-based pattern that is semi-chaotic. The system includes a wavelet/time conversion block Mλ, which is representative of a wavelet transformation of a semi-chaotic input signal, and a memory block MP which stores the wavelet coefficients generated by Mλ in an asymmetric matrix. The system further includes a predictor block MPP, which performs a time shifted symbolic operation on the memory block MP and is, therefore representative of the time shifted wavelet (Mλ). A Pattern Output block transforms the output predictor block MPP into a time-based output that is predictive of the semi-chaotic time-based input at a future point in time. First and second variables (Cp and Cpp) are automatically generated and used to compensate low (Cp) and high (Cpp) frequency components of an input.

An iterative Fourier transform unit of a modulation pattern calculation apparatus performs a Fourier transform on a waveform function including an intensity spectrum function and a phase spectrum function, performs a replacement of a temporal intensity waveform function based on a desired waveform after the Fourier transform, and then performs an inverse Fourier transform. The iterative Fourier transform unit performs the replacement using a result of multiplying a function representing the desired waveform by a coefficient. The coefficient has a value with which a difference between the function after the multiplication of the coefficient and the temporal intensity waveform function after the Fourier transform is smaller than a difference before the multiplication, and a ratio of the difference is smaller when an intensity is higher at each time of the function before the multiplication.

A method that includes operating a bus monitoring system having at least one interface configured to be coupled to at least one communication bus and receive bus traffic transmitted over the communication bus(es). The method also includes, using a device authentication system of the bus monitoring system, analyzing the bus traffic received via the at least one interface. Analyzing the bus traffic includes obtaining a message in the bus traffic (where the message identifies a source), identifying a support vector machine that corresponds to the source of the message, applying a wave transform to a waveform of the received message in order to generate a transformed waveform, inputting the transformed waveform to the identified support vector machine, and taking action in response to the identified support vector machine determining that the transformed waveform or the associated information does not correspond to the source.

A device, method, and computer readable storage medium generate a biometric public key for an individual based on both the individual's biometric data and a secret, in a manner that verifiably characterizes both while tending to prevent recovery of either by anyone other than the individual. The biometric public key may be later used to authenticate a subject purporting to be the individual, using a computing facility that need not rely on a hardware root of trust. Such biometric public keys may be distributed without compromising the individual's biometric data. In operation, a confident subset of a set of biometric values of the subject is extracted, including by performing a transform of the set of biometric values. The transform may variously be a Gabor transform, a wavelet transform, processing by a machine learning system, etc.

An iterative Fourier transform unit of a modulation pattern calculation apparatus performs a Fourier transform on a waveform function including an intensity spectrum function and a phase spectrum function, performs a replacement of a temporal intensity waveform function based on a desired waveform after the Fourier transform, and then performs an inverse Fourier transform. The iterative Fourier transform unit performs the replacement using a result of multiplying a function representing the desired waveform by a coefficient. The coefficient has a value with which a difference between the function after the multiplication of the coefficient and the temporal intensity waveform function after the Fourier transform is smaller than a difference before the multiplication, and a ratio of the difference is smaller when an intensity is higher at each time of the function before the multiplication.

The present invention belongs to the technical field of fault diagnosis of aero-engines, and provides a method for fault diagnosis of an aero-engine rolling bearing based on random forest of power spectrum entropy. Aiming at the above-mentioned defects existing in the prior art, a method for fault diagnosis of an aero-engine rolling bearing based on random forest is provided, wherein test measured data for an aero-engine rolling bearing provided by a research institute are used for establishing a training dataset and a test dataset first; and based on an idea of fault feature extraction, time domain statistical analysis and frequency domain analysis are conducted on original collection data by adopting wavelet analysis; thereby realizing effective fault diagnosis from the perspective of engineering application.

A method includes receiving electroencephalographic (EEG) signal data recordings collected from a plurality of individuals via at least one EEG monitoring device. An optimized plurality of wavelet packet atoms is constructed based on the EEG signal data recordings and a mother wavelet. The optimized plurality of wavelet packet atoms is reordered to obtain an optimal reordered set of wavelet packet atoms. The optimal reordered set of wavelet packet atoms is normalized to obtain an optimal normalized set of wavelet packet atoms that is representative of brain activities of the plurality of individuals. A particular EEG signal data recording of a particular individual is received, which is projected onto the optimal normalized set of wavelet packet atoms to obtain an individual-specific set of projections for the particular individual on the optimal normalized set of wavelet packet atoms. A brain activity representation of the particular individual is generated based on the individual-specific set of projections.

A device, method, and computer readable storage medium generate a biometric public key for an individual based on both the individual's biometric data and a secret, in a manner that verifiably characterizes both while tending to prevent recovery of either by anyone other than the individual. The biometric public key may be later used to authenticate a subject purporting to be the individual, using a computing facility that need not rely on a hardware root of trust. Such biometric public keys may be distributed without compromising the individual's biometric data. In operation, a confident subset of a set of biometric values of the subject is extracted, including by performing a transform of the set of biometric values. The transform may variously be a Gabor transform, a wavelet transform, processing by a machine learning system, etc.

A method for producing a thinned representation of vibration waveform data. The waveform vibration data is received and divided into sequential blocks. For each sequential block, each serially designated in turn as a current block, the following steps are performed. When the current block is also a first block, the current block is passed as a reference block. A representative value for the current block is computed and compared to the representative value for the reference block to determine a difference. The representative value for the current block is compared to a minimum representative value. The current block is transformed into a spectrum and compared to the spectrum for the reference block to determine a correlation value. When the representative value for the current block is above the minimum representative value, the current block is passed as the reference block whenever at least one of the following is true, (a) the first difference is greater than a given difference, (b) the correlation value is less than a given correlation value, and (c) a numerical count of blocks between the current block and a most recently passed reference block is greater than a given maximum.

The present disclosure provides a distortion-free boundary extension method for online wavelet denoising. The method includes: S1: acquiring a signal segment x.sub.n, and performing a distortion-free boundary extension on the signal segment to obtain M+N+L data; S2: decomposing a lifting wavelet of the N data to be denoised into j layers to acquire approximation coefficients and detail coefficients; S3: calculating a threshold of each layer of the lifting wavelet; S4: thresholding the detail coefficients of each layer to obtain estimated values of the detail coefficients; S5: performing wavelet reconstruction by the approximation coefficients and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal after denoising; and S6: outputting data.