Abstract: A method involves receiving power data measurements at nodes of an electrical power grid, the electrical power grid having multiple buses. For a first bus of the electrical power grid, an objective function is repeatedly minimized using the received power data measurements to determine estimated admittances between the first bus and other buses of the electrical power grid. The minimization of the objective function is linearly constrained by a repeatedly estimated sum of conductances and susceptances connected to the first bus. A minimum value of the objective function for the first bus is determined that corresponds to a maximum value of the estimated sum of conductances and susceptances. A topology of the electrical power grid associated with the first bus is determined based on the estimated admittances that correspond to the minimum value of the objective function and to the maximum value of the estimated sum of conductances and susceptances.

Abstract: In this application, a set of orthogonal functions is introduced whose power spectral densities are all rectangular shape. To find the orthogonal function set, it was considered that their spectrums (Fourier transforms of the functions) are either real-valued or imaginary-valued, which are corresponding to even and odd real-valued time domain signals, respectively. The time domain functions are all considered real-valued because they are actually physical signals. The shape of the power spectral densities of the signals are rectangular thus, the Haar orthogonal function set can be employed in the frequency domain to decompose them to several orthogonal functions. Based on the inverse Fourier transform of the Haar orthogonal functions, the time domain functions with rectangular power spectral densities can be determined. This is equivalent to finding the time-domain functions by taking the inverse Fourier transform of the frequency domain Walsh functions.

Abstract: In this application, a set of orthogonal functions is introduced whose power spectral densities are all rectangular shape. To find the orthogonal function set, it was considered that their spectrums (Fourier transforms of the functions) are either real-valued or imaginary-valued, which are corresponding to even and odd real-valued time domain signals, respectively. The time domain functions are all considered real-valued because they are actually physical signals. The shape of the power spectral densities of the signals are rectangular thus, the Haar orthogonal function set can be employed in the frequency domain to decompose them to several orthogonal functions. Based on the inverse Fourier transform of the Haar orthogonal functions, the time domain functions with rectangular power spectral densities can be determined. This is equivalent to finding the time-domain functions by taking the inverse Fourier transform of the frequency domain Walsh functions.

Abstract: The disclosure relates to improved direct digital frequency synthesizers. A synthesizer in one embodiment is comprised of an accumulator that provides a phase signal and an interpolator having two or more interpolation polynomials. The polynomial that processes the phase signal is selected by comparing the phase signal to a threshold value. A reduced complexity digital circuit is provided for implementing the improved synthesizer.