Publication

On Interpolation and Resampling of Discrete Data

Pouya Dehghani Tafti
2006
Journal Articles

Abstract

This letter introduces a new representation of discrete signals based on the mathematical notions of functionals and continuous dual spaces. A new and more general sampling theorem is also suggested. Next, the problems of interpolating and resampling discrete signals are addressed; and a general solution using functional interpolation—which is applicable to many different settings—is proposed. Families of resampling filters dubbed de Boor-Ron filters that use de Boor-Ron interpolation are introduced, and their numerical realization is discussed. Some applications of this research are suggested.

Official source

https://infoscience.epfl.ch/entities/publication/d0df7799-89c4-4877-9c0b-e25749ae3a90

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Pouya Dehghani Tafti
2006
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d0df7799-89c4-4877-9c0b-e25749ae3a90

About this result

Related concepts (32)

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Sample-rate conversion

Sample-rate conversion, sampling-frequency conversion or resampling is the process of changing the sampling rate or sampling frequency of a discrete signal to obtain a new discrete representation of the underlying continuous signal. Application areas include and audio/visual systems, where different sampling rates may be used for engineering, economic, or historical reasons. For example, Compact Disc Digital Audio and Digital Audio Tape systems use different sampling rates, and American television, European television, and movies all use different frame rates.

Related publications (32)

On Interpolation and Resampling of Discrete Data

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