scholarly journals An extended Prony’s interpolation scheme on an equispaced grid

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Dovile Karalienė ◽  
Zenonas Navickas ◽  
Raimondas Čiegis ◽  
Minvydas Ragulskis
Keyword(s):  
Interpolation Scheme ◽  
Recurrent Sequence ◽  
Minimal Order ◽  
Recurrent Function ◽  
Prony Method ◽  
Interpolation Technique ◽  
Linear Recurrent Sequence ◽  
Grid Based

AbstractAn interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension of the Prony method and can be useful for describing noisy and defected signals.

scholarly journals Artinian bimodule with quasi-Frobenius bimodule of translations

2019 ◽  
Vol 29 (2) ◽  
pp. 103-119
Author(s):  
Aleksandr A. Nechaev ◽  
Vadim N. Tsypyschev
Keyword(s):  
Commutative Ring ◽  
Recurrent Sequence ◽  
Artinian Rings ◽  
Linear Recurrent Sequence ◽  
Left And Right ◽  
Additional Assumptions

Abstract The possibility to generalize the notion of a linear recurrent sequence (LRS) over a commutative ring to the case of a LRS over a non-commutative ring is discussed. In this context, an arbitrary bimodule AMB over left- and right-Artinian rings A and B, respectively, is associated with the equivalent bimodule of translations CMZ, where C is the multiplicative ring of the bimodule AMB and Z is its center, and the relation between the quasi-Frobenius conditions for the bimodules AMB and CMZ is studied. It is demonstrated that, in the general case, the fact that AMB is a quasi-Frobenius bimodule does not imply the validity of the quasi-Frobenius condition for the bimodule CMZ. However, under some additional assumptions it can be shown that if CMZ is a quasi-Frobenius bimodule, then the bimodule AMB is quasi-Frobenius as well.

scholarly journals On the Constant in the Average Digit Sum for a Recurrence-Based Numeration

2016 ◽  
Vol 11 (2) ◽  
pp. 125-150
Author(s):  
Christian Ballot
Keyword(s):  
Positive Constant ◽  
Asymptotic Result ◽  
Elementary Approach ◽  
Recurrent Sequence ◽  
Explicit Formulas ◽  
Large Classes ◽  
Initial Term ◽  
Linear Recurrent Sequence ◽  
Positive Integers ◽  
The Greedy Algorithm

AbstractGiven an integral, increasing, linear-recurrent sequence A with initial term 1, the greedy algorithm may be used on the terms of A to represent all positive integers. For large classes of recurrences, the average digit sum is known to equal cA log n+O(1), where cA is a positive constant that depends on A. This asymptotic result is re-proved with an elementary approach for a class of special recurrences larger than, or distinct from, that of former papers. The focus is on the constants cA for which, among other items, explicit formulas are provided and minimal values are found, or conjectured, for all special recurrences up to a certain order.

scholarly journals Inter-Frame Based Interpolation for Top–Bottom Packed Frame of 3D Video

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 702
Author(s):  
Phan Van Duc ◽  
Phu Tran Tin ◽  
Anh Vu Le ◽  
Nguyen Huu Khanh Nhan ◽  
Mohan Rajesh Elara
Keyword(s):  
Missing Values ◽  
State Of The Art ◽  
Original Data ◽  
Interpolation Scheme ◽  
Interpolation Technique ◽  
Broadcasting System ◽  
Left And Right ◽  
Inter Frame ◽  
Bottom Frame

The frame-compatible packing for 3D contents is the feasible approach to archive the compatibility with the existing monocular broadcasting system. To perceive better 3D quality, the packed 3D frames are expanded to the full size at the decoder. In this paper, an interpolation technique enhancing and comparing the quality of enlarged halt vertical left and right stereo video in the top–bottom frame-compatible packing is presented. To this end, the appropriate interpolation modes from fourteen available modes for each row segment, which exploit the correlation between left and right stereoscopic as well as current and adjacent frames of individual view, are estimated at the encoder. Based on the information received from the encoder, at the decoder, the interpolation scheme can select the most appropriate available original data to find the missing values of to-be-discarded row segments. The proposed method outperformed than the state-of-the-art interpolation methods in terms of subjective visualization and numerical PSNRs and SSMI about 11%, with an execution time of about 12% comparisons.

Spatial Rainfall Pattern Identification by Optimum Interpolation Technique and Application for Turkey

2001 ◽  
Vol 32 (2) ◽  
pp. 85-98 ◽  
Author(s):  
Zekai Şen ◽  
Zeyad Habib
Keyword(s):  
Correlation Functions ◽  
Spatial Interpolation ◽  
Interpolation Method ◽  
Rainfall Variability ◽  
Monthly Rainfall ◽  
Two Dimensional ◽  
Interpolation Scheme ◽  
Spatial Estimation ◽  
Optimum Interpolation ◽  
Interpolation Technique

The spatial interpolation of hydrometeorological data aims at estimating the value of rainfall at a given site based on the observation at neighboring stations. This is a problem of operational hydrometeorology that is regularly encountered in the spatial estimation procedures. In this paper, an optimum interpolation method is validated for the analysis of monthly rainfall amounts over Turkey. Hence, a two dimensional statistically optimum interpolation scheme is generated for the analysis of monthly rainfall amounts over Turkey. Monthly spatial correlation functions are used for the analysis and modelling of the spatial monthly rainfall variability.

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