Quantitative theory of interbilayer interactions is essential to interpret x-ray scattering data and to elucidate these interactions for biologically relevant systems. For this purpose Monte Carlo simulations have been performed to obtain pressure P and positional fluctuations s. An alternative method, called Fourier Monte Carlo ~FMC!, that is based on a Fourier representation of the displaceme...

Abstract In this paper, we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) sinc as its application. The computation of NNFFT is mainly based on nodes equispaced frequencies (NFFT). employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, show that error $$\sinh$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system’s state variables...

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

Sound produced by Musical instruments with definite pitch consists of the Harmonic Series and the nonharmonic Residual. It is common to treat the Harmonic Series as the main characteristic of the timbre of pitched musical instruments. But does the Harmonic Series indeed contain the complete information required for discriminating among different musical instruments? Could the non-harmonic Resid...

In different papers dealing with automatic musical instrument recognition of pitched instruments, the features used for classification are based solely on the fundamental frequencies and the harmonic series, ignoring the nonharmonic residual. In this paper we explore whether instrument recognition rate of pitched instruments is decreased by removing the non-harmonic information present in the s...

Recently, the butterfly approximation scheme has been proposed for computing Fourier transforms with sparse and smooth sampling in frequency and spatial domain. We present a rigorous error analysis which shows how the local expansion degree depends on the target accuracy and the nonharmonic bandwidth. Moreover, we show that the original scheme becomes numerically unstable if a large local expan...