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Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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177 citations
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TL;DR: The WKB asymptotic method is applied to the calculation of cochlear models with square scala cross section, for which the fluid motion is fully three dimensional and shows quite satisfactory agreement with the experimental model results.
Abstract: The WKB asymptotic method is applied to the calculation of cochlear models with square scala cross section, for which the fluid motion is fully three dimensional. The analysis begins with the exact solution for wave propagation in a duct with constant properties. This solution is somewhat tedious but straightforward, since it requires a Fourier series expansion across the duct. Then with the formulation of Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)], the approximate solution is readily generated for the duct with properties which vary slowly along the length. Numerical calculations are carried out for the experimental models of Cannel [Ph.D. thesis, Univ. of Warwick (1969)] and Helle [Dr.-Ing. disser., Technische Univ., Muchen (1974)] who furnish quantitative details of both "basilar membrane" response and model parameters. Without any free parameters for adjusting, the present WKB solution shows quite satisfactory agreement with the experimental model results. Computer time is reasonable; the calculation of displacement envelope and phase at a number of stations along the cochlea for a given frequency requires only one second of CPU time. Thus the credibility and practically of the approach is established for the investigation of yet more realistic and more elaborate cochlear models.
176 citations
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01 Oct 1998
TL;DR: It is shown here how to identify the different types of EMTs using a 3D printer.
Abstract: Part 1 Algorithms for wavelet transforms: Haar's simple wavelets multidimensional wavelets and applications algorithms for Daubechie's wavelets. Part 2 Basic Fourier analysis: inner products and orthogonal projections discrete and fast Fourier transforms Fourier series for periodic functions. Part 3 Computation and design of wavelets: Fourier transforms on the line and space Duabechies' wavelets design signal representations with wavelets.
175 citations
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TL;DR: In this article, a two-dimensional forward modeling algorithm based on a Fourier method was proposed to handle the free surface boundary condition with a new set of wave equations which contain the stresses as unknowns instead of the displacements.
Abstract: We introduce a two-dimensional forward modeling algorithim based on a Fourier method. In order to be able to handle the free surface boundary condition with the Fourier method, a new set of wave equations are derived which contain the stresses as unknowns instead of the displacements. The solution algorithm includes a discretization in both space and time. Spatial derivatives are approximated with the use of the Fast Fourier Transform, whereas temporal derivatives are calculated with second order differencing. The numerical method is tested against the analytic solution for Lamb's problem in two dimensions.
175 citations
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TL;DR: In this paper, the authors generalize the L p es t imate of the opera tor M* in [7] to a Calderdn -Zygmund kernel defined in R', s ~_ 2, which has continuous derivatives of order s 41 outside the origin.
Abstract: T s Ts = o ( l o g l o g I~]), t~]-+ 0% for almost eve ry x in T,. I n Sections 1 to 3 in this pape r we prove among o ther things the following theorem, which generalizes the L p es t imate of the opera tor M* in [7]. TEEORE~. Assume that k is a Calderdn -Zygmund kernel defined in R', s ~_ 2, which has continuous derivatives of order ~ s 41 outside the origin. Let the operator M be defined by
174 citations