Article

# The accurate numerical inversion of laplace transforms

01/1979; DOI: 10.1093/imamat/23.1.97

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**ABSTRACT:**The rectangular power-ground structure is thoroughly analyzed in time domain. The time-dependent electric-field distribution within the power-ground structure is expanded in ray-like constituents that propagate via the reflections against circuitβs periphery. Their relation to the classical eigenfunction expansion is demonstrated. It is shown that the ray-type expansion is always exact in any finite time window of observation and can be readily generalized to account for dissipation and relaxation mechanisms. Obtained results concerning a dispersive dielectric described through finite conductivity and Debije relaxation models are discussed and validated on a number of illustrative examples.IEEE Transactions on Electromagnetic Compatibility 10/2014; 56(5):1095-1102. · 1.35 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Performance analysis of the $p$-norm detector to date has been limited to ad hoc approximations, nonfading channels, and Rayleigh fading. To overcome these limitations, we develop several analytical/numerical solutions for detection probability $P_{d}$ and false alarm probability $P_{f}$, which are necessary to specify the receiver operating characteristic (ROC) curves of the $p$-norm detector. First, for nonfading channels (additive white Gaussian noise (AWGN) only), the moment-generating function (mgf) of the decision variable is derived in two forms: 1) closed form for even integer $p$ and 2) series form for arbitrary $p$. To evaluate $P_{d}$ and $P_{f}$, a numerical method utilizing the Talbot inversion is developed for case 1, and an infinite series expansion with convergence acceleration based on the $epsilon$-algorithm is derived for case 2. As an alternative to mgf-based analysis, a Laguerre polynomial series is also used to derive new $P_{d}$ and $P_{f}$ approximations. Second, series-form mgf-based $P_{d}$ expressions are derived for $kappahbox{-}mu$ and $alphahbox{-}mu$ fading channels. Third, for antenna diversity reception, new $p$-law combining (pLC) and $p$-law selection (pLS) schemes are proposed. The performance of these combiners with the $p$-norm detector is derived for Nakagami- $m$ fading and is compared with that of the classical maximal ratio combining (MRC) and selection combining (SC). Interestingly, both pLC and pLS perform similarly to SC at low signal-to-noise ratio (SNR) but outperform it at relatively high SNR, with pLC performing closer to the optimal MRC. Numerical results are presented to verify the derived results and to provide further insights.IEEE Transactions on Vehicular Technology 01/2014; 63(7):3209-3222. · 2.64 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**New methods are proposed for the numerical evaluation of f(π) or f(π)b, where f(π) is a function such as π 1/2 or log(π) with singularities in (-β,0] and π is a matrix with eigenvalues on or near (0,β). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of f(π)b is typically reduced to one or two dozen linear system solves, which can be carried out in parallel.SIAM Journal on Numerical Analysis 01/2008; 46(5). · 1.69 Impact Factor

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