An Introduction to Sampling Analysis

Butzer, Paul L.; Schmeißer, Gerhard; Stens, R. L.

doi:10.1007/978-1-4615-1229-5_2

Cited by 84 publications

(54 citation statements)

References 100 publications

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“…Its behaviour depends on the smoothness properties of f , and was extensively studied in [1]. If f is bandlimited to [−σ, σ], then it vanishes, as to be expected.…”

Section: Introductionmentioning

confidence: 92%

Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

Butzer

Schmeißer

Stens

2012

Entropy

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The paper is concerned with Shannon sampling reconstruction formulae of derivatives of bandlimited signals as well as of derivatives of their Hilbert transform, and their application to Boas-type formulae for higher order derivatives. The essential aim is to extend these results to non-bandlimited signals. Basic is the fact that by these extensions aliasing error terms must now be added to the bandlimited reconstruction formulae. These errors will be estimated in terms of the distance functional just introduced by the authors for the extensions of basic relations valid for bandlimited functions to larger function spaces. This approach can be regarded as a mathematical foundation of aliasing error analysis of many applications.

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“…Its behaviour depends on the smoothness properties of f , and was extensively studied in [1]. If f is bandlimited to [−σ, σ], then it vanishes, as to be expected.…”

Section: Introductionmentioning

confidence: 92%

Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

Butzer

Schmeißer

Stens

2012

Entropy

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“…Since (λ, µ) ∈ C 2 and m, n are arbitrary, provided that (λ, µ) = (λ mn , µ mn ), the combination (4.6), (4.7) and (4.17) leads to the desired sampling representation for f 11 …”

Section: Theorem 41 Assume That System (31)-(36) Has No Eigenvalumentioning

confidence: 99%

Multivariate Sampling Theorems Associated With Multiparameter Differential Operators

Annaby

2005

Proceedings of the Edinburgh Mathematical Society

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We investigate the multivariate sampling theory associated with multiparameter eigenvalue problems. A several-variable counterpart of the classical sampling theorem of Whittaker, Kotel'nikov and Shannon is given. It arose when the multiparameter system has order one. Two-dimensional sampling theorems associated with two-parameter systems of second-order differential operators will be established. The sampling formulae are of multivariate non-uniform Lagrange interpolation type. Unlike many of the known formulae, the interpolating functions are not necessarily products of single variable functions.

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“…This lowers the quality measurements due to the presence of noise in a significant part of the information. More details are given in Section 3.2 and described in [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Bearing Diagnostics of Hydro Power Plants Using Wavelet Packet Transform and a Hidden Markov Model with Orbit Curves

Pino

Ribas

Guimarães

2018

Shock and Vibration

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The contribution of a medium-sized hydro power plant to the power grid can be either at base load or at peak load. When the latter is the most common operation mode, it increases the start and stop frequency, intensifying the hydro turbine components' degradation, such as the guide bearings. This happens due to more frequent operation in transient states, which means being outside the service point of the machines' nominal condition, consisting of speed, flow, and gross head. Such transient state operation increases the runner bearings' mechanical vibration. The readings are acquired during the runner start-ups and filtered by a DC component mean value and a wavelet packet transform. The filtered series are used to estimate the relationship between the maximum orbit curve displacement and the accumulated operating hours. The estimated equation associated with the ISO 7919-5 vibration standards establishes the sojourn times of the degradation states, sufficient to obtain the transition probability distribution. Thereafter, a triangular probability function is used to determine the observation probability distribution in each state. Both matrices are inputs required by a hidden Markov model aiming to simulate the equipment deterioration process, given a sequence of maximum orbit curve displacements.

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An Introduction to Sampling Analysis

Cited by 84 publications

References 100 publications

Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

Multivariate Sampling Theorems Associated With Multiparameter Differential Operators

Bearing Diagnostics of Hydro Power Plants Using Wavelet Packet Transform and a Hidden Markov Model with Orbit Curves

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