We present a simple and efficient compact fourth-order Poisson solver in polar coordinates. This solver relies on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the compact fourthorder finite difference scheme. By shifting a grid a half mesh away from the origin and incorporating the symmetry constraint of Fourier coefficients,...

We show that simple modifications to van der Hoeven's forward and inverse truncated Fourier transforms allow the algorithms be performed in-place, with only a linear overhead in complexity.

For analysis and design of water resource systems, it is sometimes useful to generate highresolution (e.g., weekly) synthetic river flows. Periodic autoregressive moving average (PARMA) time series models provide a powerful tool for generating synthetic flows. Periodically stationary models are indicated when the basic statistics (mean, variance, and autocorrelation) of the time series exhibit ...

A method is proposed to optimally design the Microstrip Nonuniform Transmission Line (MNTLs) as lowpass filters. Some electrical and physical restrictions are used to design MNTLs. To optimally design the MNTLs, their strip width is expanded as truncated Fourier series, firstly. Then, the optimum values of the coefficients of the series are obtained through an optimization approach. The perform...

Knowledge of a truncated Fourier series expansion for a discontinuous 2^-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval [-1, 1], is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in e...

Based upon new global class field concepts leading to two-dimensional global Langlands correspondences, a modular representation of cusp forms is proposed in terms of global elliptic bisemimodules which are (truncated) Fourier series over R . As application, the conjectures of Shimura-Taniyama-Weil, Birch-Swinnerton-Dyer and Riemann are analyzed.

A new integration method for highly oscillating circuits is proposed. The method is based on using finite (truncated) Fourier series for representation of signals. Nonlinear transformations are implemented in two phases: harmonic linearization using only one sine wave in phase space, and general Chebyshev transformation of waveforms to return into true time domain.