About: Window function is a(n) research topic. Over the lifetime, 3773 publication(s) have been published within this topic receiving 47518 citation(s). The topic is also known as: Windowed frame & Hanning filter.
Abstract: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.
Topics: Kernel (statistics) (58%), Diffuse element method (57%), Meshfree methods (56%) ...read more
01 Nov 2014-Astronomy and Astrophysics
Abstract: This paper characterizes the effective beams, the effective beam window functions and the associated errors for the Planck High Frequency Instrument (HFI) detectors. The effective beam is the angular response including the effect of the optics, detectors, data processing and the scan strategy. The window function is the representation of this beam in the harmonic domain which is required to recover an unbiased measurement of the cosmic microwave background angular power spectrum. The HFI is a scanning instrument and its effective beams are the convolution of: a) the optical response of the telescope and feeds; b) the processing of the time-ordered data and deconvolution of the bolometric and electronic transfer function; and c) the merging of several surveys to produce maps. The time response transfer functions are measured using observations of Jupiter and Saturn and by minimizing survey difference residuals. The scanning beam is the post-deconvolution angular response of the instrument, and is characterized with observations of Mars. The main beam solid angles are determined to better than 0.5% at each HFI frequency band. Observations of Jupiter and Saturn limit near sidelobes (within 5 degrees) to about 0.1% of the total solid angle. Time response residuals remain as long tails in the scanning beams, but contribute less than 0.1% of the total solid angle. The bias and uncertainty in the beam products are estimated using ensembles of simulated planet observations that include the impact of instrumental noise and known systematic effects. The correlation structure of these ensembles is well-described by five errors eigenmodes that are sub-dominant to sample variance and instrumental noise in the harmonic domain. A suite of consistency tests provide confidence that the error model represents a sufficient description of the data. The total error in the effective beam window functions is below 1% at 100 GHz up to multiple l similar to 1500, below 0.5% at 143 and 217 GHz up to l similar to 2000.
01 Jan 1993-
Abstract: We present a straightforward and robust algorithm for periodicity detection, working in the lag (autocorrelation) domain. When it is tested for periodic signals and for signals with additive noise or jitter, it proves to be several orders of magnitude more accurate than the methods commonly used for speech analysis. This makes our method capable of measuring harmonics-to-noise ratios in the lag domain with an accuracy and reliability much greater than that of any of the usual frequency-domain methods. By definition, the best candidate for the acoustic pitch period of a sound can be found from the position of the maximum of the autocorrelation function of the sound, while the degree of periodicity (the harmonics-to-noise ratio) of the sound can be found from the relative height of this maximum. However, sampling and windowing cause problems in accurately determining the position and height of the maximum. These problems have led to inaccurate timedomain and cepstral methods for pitch detection, and to the exclusive use of frequency-domain methods for the determination of the harmonics-to-noise ratio. In this paper, I will tackle these problems. Table 1 shows the specifications of the resulting algorithm for two spectrally maximally different kinds of periodic sounds: a sine wave and a periodic pulse train; other periodic sounds give results between these. Table 1. The accuracy of the algorithm for a sampled sine wave and for a correctly sampled periodic pulse train, as a function of the number of periods that fit in the duration of a Hanning window. These results are valid for pitch frequencies up to 80% of the Nyquist frequency. These results were measured for a sampling frequency of 10 kHz and window lengths of 40 ms (for pitch) and 80 ms (for HNR), but generalize to other sampling frequencies and window lengths (see section 5).
Abstract: This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.
Topics: Kernel (statistics) (58%), Window function (56%), Smoothed-particle hydrodynamics (53%) ...read more
James D. Johnston1•Institutions (1)
09 Apr 1980-
Abstract: This paper discusses a family of filters that have been designed for Quadrature Mirror Filter (QMF) Banks. These filters provide a significant improvement over conventional optimal equiripple and window designs when used in QMF banks. The performance criterion for these filters differ from those usually used for filter design in a way which makes the usual filter design techniques difficult to apply. Two filters are actually designed simultaneously, with constraints on the stop band rejection, transition band width, and pass and transition band performance of the QMF filter structure made from those filters. Unlike most filter design problems, the behavior of the transition band is constrained, which places unusual requirements on the design algorithm. The requirement that the overall passband behavior of the QMF bank be constrained (which is a function of the passband and stop band behavior of the filter) also places very unusual requirements on the filter design. The filters were designed using a Hooke and Jeaves optimization routine with a Hanning window prototype. Theoretical results suggest that exactly flat frequency designs cannot be created for filter lengths greater than 2, however, using the discussed procedure, one can obtain QMF banks with as little as ±.0015dB ripple in their frequency response. Due to the nature of QMF filter applications, a small set of filters can be derived which will fit most applications.