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A MONOTONIC CONVOLUTION FOR MINKOWSKI SUMS
International Journal of Computational Geometry & Applications, 2007 We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution.
Victor Milenkovic, Elisha Sacks
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Ramanujan’s convolution sum twisted by Dirichlet characters
International Journal of Number Theory, 2019 We find formulas for convolutions of sum of divisor functions twisted by the Dirichlet character [Formula: see text], which are analogous to Ramanujan’s formula for convolution of usual sum of divisor functions. We use the theory of modular forms to prove our results.
Aygin, Zafer Selcuk, Hong, Nankun
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Evaluation of certain convolution sums involving the sum of the divisors function
Ramanujan Journal, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bulent KÖKLÜCE
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Distributional Behavior of Convolution Sum System Representations
IEEE Transactions on Signal Processing, 2018In this paper, we study the validity of the usual convolution sum sampling representation of linear time-invariant (LTI) systems. We consider continuous input signals with finite energy that are absolutely integrable and vanish at infinity. Even for these benign signals, the convolution sum does not always converge.
Holger Boche, Ullrich J Monich
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Non-Existence of Convolution Sum System Representations
IEEE Transactions on Signal Processing, 2019Convolution sum system representations are commonly used in signal processing. It is known that the convolution sum, treated as the limit of its partial sums, can be divergent for certain continuous signals and stable linear time-invariant (LTI) systems, even when the convergence of the partial sums is treated in a distributional setting. In this paper,
Holger Boche +2 more
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Evaluate the Convolution Integral and Convolution Sum Use Compact Formula
2011 7th International Conference on Wireless Communications, Networking and Mobile Computing, 2011Abstract: Convolution integral and convolution summation play an important role in the analysis of the linear time invariant systems. At present, many text books have published in my home country or foreign country , especially the ?sSignals and Systems?t all discuss the methods by use of the graph to determine the up limit, low limit and the interval ...
Bin Ren, De-yong Yu
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A sharp discrete convolution sum estimate
Communications in Nonlinear Science and Numerical Simulation, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin Stynes, Dongling Wang
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