Journal ArticleDOI
Interpolation by fast Fourier and Chebyshev transforms
TLDR
Transform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms, which produce an interpolation passing directly through the given values and are applied easily to the multi-dimensional case.Abstract:
Transform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms. For periodic data adequately sampled, the fast Fourier transform (FFT) is used directly. With undersampled or aperiodic data, a Chebyshev interpolating polynomial is evaluated by means of the FFT to provide minimum deviation and distributed ripple. The merits of two kinds of Chebyshev series are compared. All the methods described produce an interpolation passing directly through the given values and are applied easily to the multi-dimensional case.read more
Citations
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Automatic ECG Analysis using Principal Component Analysis and Wavelet Transformation
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Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations
TL;DR: The IMAC Math-Quantum Day, Universitat Jaume I, Castellon, Spain, September 27, 2019, will be the first event of its kind in Europe and will focus on quantum mechanics and its applications in medicine, science and engineering.
Journal ArticleDOI
Interpolation methods for surface mapping.
TL;DR: Methods for preparation of three dimensional information for isoline mapping are described based on Fourier, Chebyshev, and cubic interpolation from regularly spaced arrays of spatial data.
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Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations
TL;DR: In this article, a large family of distributions can be encoded as low-entanglement states of the quantum register, which can be efficiently created in a quantum computer, but they are also efficiently stored, manipulated and probed using Matrix-Product States techniques.
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Algorithm 749: fast discrete cosine transform
TL;DR: An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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Discrete Cosine Transform
TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.
Journal ArticleDOI
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
TL;DR: This second part of the paper shows how the cosine transformation can be computed by a modification of the fast Fourier transform and all three problems overcome.
Journal ArticleDOI
Teminology in digital signal processing
Lawrence R. Rabiner,J.W. Cooley,H. Helms,Leland B. Jackson,J. Kaiser,C. Rader,R. W. Schafer,Kenneth Steiglitz,C. Weinstein +8 more
TL;DR: This paper proposes terminology for use in papers and texts on digital signal processing which it is felt is self-consistent, and which is in reasonably good agreement with current practices.