A general tool for circuit analysis based on wavelet transform

Innovative model for time-varying power line communication channel response evaluation

“…The cable parameters are the following: (19) , while the loads , , and considered purely resistive are supposed to vary in the interval . The variation of an eventually present reactive part of the impedances can be straightforwardly treated in the wavelet-domain, as shown in [17]- [20]. Obviously, there is an increase in the number of the equivalent sources that constitute the modified vector of the input signals, as shown in (14).…”

“…The authors have used the WE tool for the numerical analysis of electric circuits [17], transmission lines [18], and general time-domain problems [19], obtaining excellent results. Recently, wavelet bases have been used to give a two-port representation (in the wavelet-domain) of printed circuit board (PCB) discontinuities [20], offering an innovative and powerful contribution to this area: the representation of an electric/electronic device by a scattering parameters matrix in the wavelet-domain.…”

“…We have ascertained that the Daubechies Wavelets on the interval for which the representation of differential and integral operators has been found [17], are the most suitable wavelet bases for this kind of problems. They are orthonormal wavelet bases, characterized by a number of vanishing moments [14], and we have focused our attention on a basis characterized by six vanishing moments, since they offer the best efficiency in terms of accuracy versus calculation time.…”

“…Since the main interest is to calculate the bounds of the voltage at the node of interest, it is straightforward to use the relation which relates the scattering parameters with the voltage (17) Hence, when we have obtained the upper and lower bounds of the power waves and , it is possible to obtain the bounds of the voltages as (18) At the end of the procedure the vectors of the voltage bounds need to be inverse transformed to give the time-domain bounds.…”

A Wavelet Operator on the Interval in Solving Maxwell's Equations

“…In [3,4] corrective coefficients have been obtained allowing the representation of functions on an interval. Wavelets on the interval in [0,1] are considered and also used to represent differential operators [3,4,6,7]. Grid point values of the first derivative of a known tabulated function are generated by introducing a suitable differentiation matrix D. In [1], the set of non-zero coefficients, which allows to determine the spatial differential operator d dx as the solution of a system of linear algebraic equations, is obtained.…”