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About 4,653 papers for “Delta operator”

Delta and Theta Operator Expansions

Alessandro Iraci, Marino Romero · arXiv (Cornell University) · 2022

We give an elementary symmetric function expansion for $MΔ_{m_γe_1}Πe_λ^{\ast}$ and $MΔ_{m_γe_1}Πs_λ^{\ast}$ when $t=1$ in terms of what we call $γ$-parking functions and lattice $γ$-parking functions. Here, $Δ_F$ and $Π$ are certain eigenoperators of the modified Macdonald basis and $M=(1-q)(1-t)$. Our main results in turn give an elementary basis expansion at $t=1$ for symmetric functions of the form $M Δ_{Fe_1} Θ_{G} J$ whenever $F$ is expanded in terms of monomials, $G$ is expanded in terms of the elementary basis, and $J$ is expanded in terms of the modified elementary basis $\{Πe_λ^\ast\}_λ$. Even the most special cases of this general Delta and Theta operator expression are significant; we highlight a few of these special cases. We end by giving an $e$-positivity conjecture for when $t$ is not specialized, proposing that our objects can also give the elementary basis expansion in the unspecialized symmetric function.

Cited by 0Open access

Prediction using the Delta Operator

M. Rostgaard, Morten Bach Lauritsen, Niels Kjølstad Poulsen · Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) · 1994

Cited by 0

Delta and Theta Operator Expansions

Alessandro Iraci, Marino Romero · Forum of Mathematics Sigma · 2024

Abstract We give an elementary symmetric function expansion for the expressions $M\Delta _{m_\gamma e_1}\Pi e_\lambda ^{\ast }$ and $M\Delta _{m_\gamma e_1}\Pi s_\lambda ^{\ast }$ when $t=1$ in terms of what we call $\gamma $ -parking functions and lattice $\gamma $ -parking functions. Here, $\Delta _F$ and $\Pi $ are certain eigenoperators of the modified Macdonald basis and $M=(1-q)(1-t)$ . Our main results, in turn, give an elementary basis expansion at $t=1$ for symmetric functions of the form $M \Delta _{Fe_1} \Theta _{G} J$ whenever F is expanded in terms of monomials, G is expanded in terms of the elementary basis, and J is expanded in terms of the modified elementary basis $\{\Pi e_\lambda ^\ast \}_\lambda $ . Even the most special cases of this general Delta and Theta operator expression are significant; we highlight a few of these special cases. We end by giving an e -positivity conjecture for when t is not specialized, proposing that our objects can also give the elementary basis expansion in the unspecialized symmetric function.

Cited by 2Open access

Delta-operator generalized predictive control (DGPC)

R. Neumann, Didier Dumur, P. Boucher · 2005

The authors present a version of the discrete time generalized predictive controller called DGPC, using the delta operator. The delta operator is introduced to overcome numerical problems which appear in discrete time models with very small sampling periods (oversampling). A polynomial approach is developed for the DGPC controller using transfer functions, with the advantages of quicker real-time computation and the possibility of stability analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 9

Effect of Delta Operator on Umbral Composition in Finite Operator calculus

A Maheswaran, C Elango · JOURNAL OF ADVANCES IN MATHEMATICS · 2016

The main objective of this paper is to propose the matrix representation of umbral composition and investigate the effect of delta operator on umbral composition by using the sequential representation of delta operator in finite operator calculus.

Cited by 0Open access

DELTA OPERATOR-BASED LATTICE FAULT DETECTION FILTER

Guobing Li · 1994

In this paper, based on Delta Operator, signal vectors of Hilbert space are constructed, an input-output model is derived, and both the forward and backward prediction error vectors are described. With the help of Lattice filters, recursive algorithms for generating time-updated as well as order-updated residual series are formed, so that a fault detection filter is designed. Combined with the approach of adaptive noise canceling, real time, on-line fault detection is carried out. Finally.simulating experiments show that this fault detection method is effective.

Cited by 0

Root distribution of delta-operator formulated polynomials

Kamal Premaratne, S. Touset, E.I. Jury · IEE Proceedings - Control Theory and Applications · 2000

Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted&apos; circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden–Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden–Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.

Cited by 4

On delta-extension for a Noether operator

Ecclésiaste Tompé Weimbapou, Abdourahman, Emmanuel Kengne · Izvestiya Vysshikh Uchebnykh Zavedenii Matematika · 2021

Изучается интегральное уравнение третьего рода в классе обобщенных функций. Показывается, что рассматриваемое уравнение обладает схожими свойствами разрешимости, что и уравнение Фредгольма второго рода.

Cited by 2

Delta operator realizations of direct-form IIR filters

J. Kauraniemi, T.I. Laakso, I. Hartimo et al. · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · 1998

The use of the delta operator in the realizations of digital filters has recently gained interest due to its good finite-word-length performance under fast sampling. We studied efficient direct form structures, and show that only some of them can be used in delta configurations, while others are evidently unstable. In this paper, we focus on the roundoff noise analysis. Of all the direct-form structures, the direct form II transposed (DFIIt) delta structure has the lowest quantization noise level at its output. This structure outperforms both the conventional direct-form (delay) structures, as well as the state-space structures for narrow-band low-pass filters with respect to output roundoff noise. Excellent roundoff noise performance is achieved at the cost of only a minor additional implementation complexity when compared with the corresponding delay realization. Complexity of a signal processor implementation of the DFIIt delta structure, which was found to be the most suitable delta structure for signal processors, is compared with those of the direct form and state-space delay structures. In addition, some hardware implementation aspects are discussed, including the minimization of the internal word length.

Cited by 82

Periodic output feedback control for Delta operator systems

B. Bandyopadhyay, P. S. Lal Priya · 2013

This paper proposes an algorithm for periodic output feedback (POF) control for Delta operator systems. The Delta operator creates the rapprochement between analog and discrete dynamic system models and establishes the natural framework to investigate the behavior of discrete dynamic models with fast sampling rates. It is shown here that, the periodic output feedback control fails for discrete-time systems represented by the traditional shift operator for smaller values of sampling time, whereas the same is possible if it is represented in the delta domain. Since the proposed algorithm is based on output feedback, it is more practical in comparison to the state feedback based control algorithms. The design method is illustrated through a numerical example and the simulation results show the effectiveness of the proposed method.

Cited by 5