Two-dimensional nonseparable perfect reconstruction (PR) filter bank design based on the Bernstein polynomial approximation

1994 ◽  
Author(s):  
Kerem A. Harmanci ◽  
Emin Anarim ◽  
Hakan Caglar ◽  
Bulent Sankur
Author(s):  
Octav Olteanu

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.


Author(s):  
Kosuke Furuya ◽  
Shintaro Hara ◽  
Kenta Seino ◽  
Shogo Muramatsu

This paper proposes a boundary operation technique of two-dimensional (2D) non-separable oversampled lapped transforms (NSOLT). The proposed technique is based on a lattice structure consisting of the 2D separable block discrete cosine transform and non-separable redundant support-extension processes. The atoms are allowed to be anisotropic with the oversampled, symmetric, real-valued, compact-supported, and overlapped property. First, the blockwise implementation is developed so that the atoms can be locally controlled. The local control of atoms is shown to maintain perfect reconstruction. This property leads an atom termination (AT) technique as a boundary operation. The technique overcomes the drawback of NSOLT that the popular symmetric extension method is invalid. Through some experimental results with iterative hard thresholding, the significance of AT is verified.


Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 956 ◽  
Author(s):  
Owoicho E. Ijiga ◽  
Olayinka O. Ogundile ◽  
Ayokunle D. Familua ◽  
Daniel J. J. Versfeld

The advancement in wireless communication applications encourages the use of effective and efficient channel estimation (CE) techniques because of the varying behaviour of the Rayleigh fading channel. In most cases, the emphasis of most proposed CE schemes is to improve the CE performance and complexity for ensuring quality signal reception and improved system throughput. Candidate waveforms whose designs are based on filter bank multi-carrier (FBMC) modulation techniques such as filter bank orthogonal frequency division multiplexing based on offset quadrature amplitude modulation (OFDM-OQAM), universal filtered multicarrier (UFMC) and generalised frequency division multiplexing based on offset quadrature amplitude modulation (GFDM-OQAM) are no exception to the use of these proposed CE techniques in the literature. These schemes are considered as potential waveform candidates for the physical/media access control layer of the emerging fifth generation (5G) networks. Therefore, pinpoint CE techniques represent an important requirement for these waveforms to attain their full potentials. In this regard, this paper reviews the concept of CE as applicable to these waveforms as well as other waveform candidates under consideration in the emerging 5G networks. Since the design of the majority of the waveform candidates is filter based, a review of the general filter design considerations is presented in this paper. Secondly, we review general CE techniques for candidate waveforms of next generation networks and classify some of the studied CE techniques. In particular, we classify the CE schemes used in filter bank OFDM-OQAM and GFDM-OQAM based transceivers and present a performance comparison of some of these CE schemes. Besides, the paper reviews the performances of two linear CE schemes and three adaptive based CE schemes for two FBMC based waveform candidates assuming near perfect reconstruction (NPR) and non-perfect reconstruction (Non-PR) filter designs over slow and fast frequency selective Rayleigh fading channels. The results obtained are documented through computer simulations, where the performances of the studied CE schemes in terms of the normalised mean square error (NMSE) are analysed. Lastly, we summarise the findings of this work and suggest possible research directions in order to improve the potentials of the studied candidate waveforms over Rayleigh fading channels.


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