Some new aspects of rational interpolation
Mathematics of Computation
Discrete-time signal processing
Discrete-time signal processing
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
EURASIP Journal on Applied Signal Processing
Canceling and selecting partials from musical tones using fractional-delay filters
Computer Music Journal
Optimal variable fractional delay filters in time-domain L-infinity norm
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Functionally weighted lagrange interpolation of band-limited signals from nonuniform samples
IEEE Transactions on Signal Processing
Block-Based Methods for the Reconstruction of Finite-Length Signals From Nonuniform Samples
IEEE Transactions on Signal Processing
Convolution-Based Trigonometric Interpolation of Band-Limited Signals
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Interpolation of Bounded Bandlimited Signals and Applications
IEEE Transactions on Signal Processing
Nonuniform Sampling of Periodic Bandlimited Signals
IEEE Transactions on Signal Processing - Part I
IEEE Transactions on Signal Processing - Part I
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This paper proposes a method to convert a fixed instant interpolator for band-limited signals into a variable instant one, which has the form of a barycentric interpolator. This interpolator makes it possible to approximate the signal and its derivatives with minimal complexity in a range that surrounds the initial instant, and is applicable to uniform and nonuniform sampling grids. The barycentric form of the interpolator is derived using two different procedures, first by the repeated use of Bernstein's inequality and Taylor's theorem, and second by truncating a Lagrange-type series. These procedures show that the proposed method can be applied to existing fixed instant interpolators, and that it can be accurate in long time intervals. Finally, an evaluation procedure for barycentric interpolators and their derivatives is presented that minimizes the number of divisions, solving at the same time the numerical problems associated with small denominators. This paper includes several numerical examples.