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We present a new method for constructing local orthogonal bases, both in continuous and discrete time. The approach is very general and can handle a large variety of cases interesting for the applications.
Riccardo Bernardini
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Proceedings., International Conference on Image Processing, 2002
Discrete-time cosine modulated filter banks, or modulated lapped transforms (MLT), have been in use for some time. Due to a few of their properties, they have become quite popular. For example, all filters (basis functions) of a filter bank are obtained by appropriate modulation of a single prototype filter.
Riccardo Bernardini, Jelena Kovacevic
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Discrete-time cosine modulated filter banks, or modulated lapped transforms (MLT), have been in use for some time. Due to a few of their properties, they have become quite popular. For example, all filters (basis functions) of a filter bank are obtained by appropriate modulation of a single prototype filter.
Riccardo Bernardini, Jelena Kovacevic
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Approximation based on orthogonal and almost orthogonal functions
Journal of the Franklin Institute, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dragan Antic +4 more
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On Orthogonal Coding-Based Modulation
IEEE Communications Letters, 2020In this letter, we propose a new orthogonal coding-based modulation (OCBM) scheme, in which all available transmitting subcarriers and antennas are activated at a time instant to transmit the data constellation symbols, and the indices of the activated subcarriers and antennas are also harnessed to carry information bits.
Junfeng Wang 0006 +8 more
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A novel orthogonal PSO algorithm based on orthogonal diagonalization
Swarm and Evolutionary Computation, 2018Abstract One of the major drawbacks of the global particle swarm optimization (GPSO) algorithm is zigzagging of the direction of search that leads to premature convergence by falling into local minima. In this paper, a new algorithm named orthogonal PSO (OPSO) algorithm is proposed that not only alleviates the associated problems in GPSO algorithm ...
Al-Bahrani, Loau Tawfak +1 more
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Mathematics of the USSR-Izvestiya, 1970
The following theorem is proved: Given any interval , there is an orthonormal system defined on [0,1] which is a basis in for all , but is not a basis in for any . Here .
Ryazanov, B. V., Slepchenko, A. N.
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The following theorem is proved: Given any interval , there is an orthonormal system defined on [0,1] which is a basis in for all , but is not a basis in for any . Here .
Ryazanov, B. V., Slepchenko, A. N.
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Authenticated QKD Based on Orthogonal States
International Journal of Theoretical Physics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiaoling Xiong +5 more
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1998
Abstract One important use of the standard inner product of ℝ 3 is that it allows us to distinguish between ‘nice’ bases such as the usual one where the basis vectors are orthogonal to each other and each has length 1, and others such as (1, 0, 0)T, (1, 1, 0)T, (1, 1, 1)T where this is not true.
Richard Kaye, Robert Wilson
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Abstract One important use of the standard inner product of ℝ 3 is that it allows us to distinguish between ‘nice’ bases such as the usual one where the basis vectors are orthogonal to each other and each has length 1, and others such as (1, 0, 0)T, (1, 1, 0)T, (1, 1, 1)T where this is not true.
Richard Kaye, Robert Wilson
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MDS codes based on orthogonality of quasigroups
Applicable Algebra in Engineering, Communication and Computing, 2023This paper presents a construction of maximum distance separable (MDS) codes through the use of orthogonal systems of \(k\)-ary quasigroup operations, including the concept of extended \(i\)-invertibility. The authors build on established results in quasigroup theory and multivariate polynomial systems to construct recursive linear MDS codes over ...
Satish Kumar +3 more
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Local orthogonal bases I: Construction
Multidimensional Systems and Signal Processing, 1996The authors present a unified approach to the construction of local orthogonal bases in the continuous and discrete multivariate setting by using symmetry properties of basis functions. Examples for one- and two-dimensional, discrete and continuous cases are included.
BERNARDINI, Riccardo, kovacevic j.
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