An extension of the notion of the analytical signal to multidimensional signals is presented The real and imaginary parts of this signal are a linear combination of the original signal and of its complete and partial Hilbert transforms Its Fourier image exists only in one orthant of the multidimensional frequency space The orthant is a half-axis in one dimension, a quadrant in two dimensions, an octant in three dimensions, etc A multidimensional complex signal makes it possible to introduce the definitions of instantaneous amplitude, instantaneous phase, and partial instantaneous complex frequencies (partial derivatives of the instantaneous phase) and to formulate a modulation theory of a multidimensional harmonic carrier The 2-D equivalent of 1-D single-sideband modulation is defined and called single quadrant modulation It is shown that the multidimensional complex signal with a signal orthant spectrum may be defined as a convolution of the real signal with the multidimensional complex delta distribution >

Multidimensional complex signals with single-orthant spectra

A fast band-limited signal extrapolation technique is presented where the total extrapolation process is achieved by a single matrix operation. The proposed technique and its implementation has many advantages over known extrapolation techniques in terms of computational savings and accuracy of the results, and it can he operated on a realtime basis.

An approach to band-limited signal extrapolation: The extrapolation matrix

Synchrophasor estimation is typically performed by means of spectral analysis based on the discrete Fourier transform (DFT). Traditional DFT approaches, though, suffer from several uncertainty contributions due to the stationarity assumption, spectral leakage effects, and the finite-grid resolution. This paper addresses these limitations, by proposing a joint application of the Hilbert transform (HT) and the interpolated DFT (IpDFT) technique. Specifically, the HT enables the suppression of the spectral leakage generated by the negative image of the tones under analysis, whereas the IpDFT limits the effects of spectrum granularity. In order to relax the constraint in terms of measurement reporting latency, the proposed estimator can adopt a window length of 40 ms and yet provides a noticeable estimation accuracy with a worst-case total vector error and frequency error equal to 0.02% and 4 mHz, respectively, in steady-state conditions. In this context, this paper discusses the most suitable setting of the algorithm parameters and their effect on spurious component rejection. Moreover, a thorough metrological characterization of the algorithm estimation accuracy and responsiveness with respect to the IEEE Std. C37.118.1 is carried out in order to detect the main uncertainty sources as well as possible room for enhancement. Finally, a comparison with two consolidated IpDFT approaches shows the actual performance enhancement provided by the proposed algorithm.

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Reduced Leakage Synchrophasor Estimation: Hilbert Transform Plus Interpolated DFT

Multidimensional Complex Signals with Single-Orthant Spectra

This paper presents three intelligent methods for condition monitoring of induction motors in real-time. A structured neural network has been designed to prognosis of instantaneous faults. The inputs of neural network are the standard deviation and mean of feature signal obtained by Hilbert transform of one phase current signal. The stator related faults have been diagnosed by designing fuzzy logic. The amplitudes of three phase currents have been given to fuzzy logic and the condition of stator has been diagnosed. The last algorithm uses the phase space of the Hilbert transform of one phase current and detects broken rotor bar faults using negative selection algorithm. The contribution of the algorithm is the development of synchronously worked algorithms, optimized for low-cost Field Programmable Gate Array (FPGA) implementation. Extensive simulations were applied to test the performance of each algorithm, and the results show that the algorithms give high accuracy in detecting whether a possible fault has occurred in any component of the motor. The average detection time of the faults is above within 2 milliseconds or less.

FPGA based intelligent condition monitoring of induction motors: Detection, diagnosis, and prognosis

A discrete filtering technique based on circular convolution is presented. The discrete Hilbert transform (DHT), in matrix form and other matrices for filtering by circular convolution, is shown to compare favorably with DFT and FFT filtering. The comparison is presented in terms of error accumulation.

https://www.ruor.uottawa.ca/bitstream/10393/11097/1/DC52487.PDF

Discrete Hilbert transform filtering

A discrete filtering technique based on the discrete Hilbert Transform (DHT) is presented. The filtering method and its implementation are shown to compare favorably with DFT and FFT filtering. The comparison is presented in terms of complexity of hardware implementation and error accumulation. The DHT itself and derived discrete filter transforms are each presented in matrix form and may be implemented with the same hardware in either series or parallel form. In this manner a large variety of filtering characteristics may be implemented by changes of the stored coefficients only. While the filtering process is a circular convolution, direct convolution filters are obtainable also, by using one row of the matrix only, and are realizable in the form of an FIR (non-recursive) digital filter.

W. Steenaart

Papers

Discrete Hilbert transform filtering

Discrete Hilbert transform filtering