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...

Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [−1, 1], as well as new results on [−1, 1]. In particular, compact formulas for the fu...

The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Padé and other interpolation schemes. A unified view of these various interpolation techniques is eloquently expressed in terms of the concept of the spectral basis of a factor ring of polynomials. When these methods are applied to th...

In the paper, the Lagrange geometric interpolation by spatial rational cubic Bézier curves is studied. It is shown that under some natural conditions the solution of the interpolation problem exists and is unique. Furthermore, it is given in a simple closed form which makes it attractive for practical applications. Asymptotic analysis confirms the expected approximation order, i.e., order six. ...

Cumulative chord C piecewise-cubics, for unparameterized data from regular curves in R , are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C piecewise-cubic interpolant. Theoretical estimates of orders of approximation are establis...

Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L*a*b*. In the present report we survey some of the most important methods of scattered data interpolation in two-dimensional and in three-dimensional...

The channel estimation techniques for OFDM systems based on pilot arrangement are investigated. The channel estimation based on comb type pilot arrangement is studied through different algorithms for both estimating channel at pilot frequencies and interpolating the channel. The estimation of channel at pilot frequencies is based on LS and LMS while the channel interpolation is done using linea...

This article presents a comparison of different interpolation techniques both in the spatial and frequency domains. Various methods are presented, from a very simple linear interpolation to more complex cubic convolution. The Fourier analysis is used to compare the methods in the frequency domain. Methods are compared by doubling the images in both spatial directions and calculating the signal-...

Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [−1, 1], as well as new results on [−1, 1]. In particular, compact formulas for the fu...