Let / ( x ) be a function of x, with the period 2ir , which takes on known values, determined by physical measurement or otherwise, at 2n + 1 points equally spaced throughout a period. It is well known that a finite trigonometric sum, of the «th order at most, which coincides with f (x) at the points in question, is given by formulae analogous to those which characterize the Fourier's developme...

We have implemented an open-source additive synthesizer in the matlab language that reads sinusoidal models from SDIF files and synthesizes them with a variety of methods for interpolating frequency, amplitude, and phase between frames. Interpolation techniques currently implemented include linear frequency and amplitude ignoring all but initial phase, dB scale amplitude interpolation, stair-st...

In this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6VBP ) by using the hyperbolic uniform spline of order 3 (lower order). Thereis proved to be first-order convergent. Numerical results confirm the order of convergencepredicted by the analysis.  

Single sensor digital cameras capture one color value for every pixel location. The remaining two color channel values need to be estimated to obtain a complete color image. This process is called demosaicing or Color Filter Array (CFA) interpolation. We propose a directional approach to the CFA interpolation problem that makes use of multiscale color gradients .The relationship between color g...

In this paper, we propose two adaptive interlaced-to-progressive conversion techniques in which the adequacy of the estimated motion vector is evaluated. If the motion vector is unlikely to give a good temporal motion compensated interpolation result, spatial interpolation is favored or selected to avoid temporal artifacts. In the rst proposed interlaced-to-progressive conversion technique, cal...

In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...

For a property measured at several locations, interpolation algorithms provide a unique and smooth function yielding a locally realistic estimation at any point within the sampled region. Previous studies searching for optimal interpolation strategies by measuring cross-validation error have not found consistent rankings; this fact was traditionally explained by differences in the distribution,...

We solve a recent conjecture, proving that the Lebesgue constant of Chebyshev-like angular nodes for trigonometric interpolation on a subinterval [−ω, ω] of the full period [−π, π] is attained at ±ω, its value is independent of ω and coincides with the Lebesgue constant of algebraic interpolation at the classical Chebyshev nodes in (−1, 1). 2000 AMS subject classification: 42A15, 65T40.