1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind

Pavlović, Vlastimir D.; Doncov, Nebojsa; Ćirić, Dejan

doi:10.1080/00207217.2013.764549

Cited by 30 publications

(38 citation statements)

References 25 publications

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“…This paper presents the further generalization of the previous research [5][6][7] in two dimensions. The proposed solution is a filter function in the z1 domain, and the Hilbert transformer in the z2 domain.…”

Section: Introductionmentioning

confidence: 82%

Shape of impulse response characteristics of linear-phase nonrecursive 2D FIR filter function

2013

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An analytical method for the new class of linear-phase multiplierless 2D FIR filter functions generated by applying the Christoffel-Darboux formula for classical Chebyshev polynomials of the first and the second kind, proposed in [6] was used for designing of linear-phase multiplierless 2D FIR filter described in this paper. Correct transformation from continuous two-dimensional domain into the z domains without residuum and without errors is described. The proposed solution high selectivity is a filter function in the z1 domain, and the Hilbert transformer in the z2 domain. The impulse response coefficients of proposed 2D FIR filter functions are presented in this paper, and corresponding examples of impulse response are illustrated. The paper also presents detailed analysis of the size of pass-band and stop-band of proposed multiplierless linearphase 2D FIR filter function. Normalized surface area of the filter function pass-band is 3.45789156 10-5 for given maximal attenuation of 0.28 dB. Normalized surface area of the filter function stop-band is 80.395% for the given minimal attenuation of 100 dB.

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Section: Introductionmentioning

confidence: 82%

Shape of impulse response characteristics of linear-phase nonrecursive 2D FIR filter function

2013

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“…Similarly, the work in [35] uses the systolic structures but focuses on replacing the original adder unit by using a parallel prefix adder (PPA) with minimal depth algorithm. Poly-phase decomposition has been used to design high-speed and low-power parallel filters [36], [7], [37], [38], [39], [40]. A modification of poly-phase decomposition is the Fast FIR algorithm (FFA).…”

Section: Introductionmentioning

confidence: 99%

Technology - Dependent Optimization of FIR Filters based on Carry - Save Multiplier and 4:2 Compressor unit

Khurshid¹,

Naaz²

2017

ELS

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43 Abstract -This work presents an FPGA implementation of FIR filter based on 4:2 compressor and CSA multiplier unit. The hardware realizations presented in this paper are based on the technology-dependent optimization of these individual units. The aim is to achieve an efficient mapping of these isolated units on Xilinx FPGAs. Conventional filter implementations consider only technology-independent optimizations and rely on Xilinx CAD tools to map the logic onto FPGA fabric. Very often this results in inefficient mapping. In this paper, we consider the traditional CSA-4:2 compressor based FIR filters and restructure these units to achieve improved integration levels. The technology optimized Boolean networks are then coded using instantiation based coding strategies. The Xilinx tool then uses its own optimization strategies to further optimize the networks and generate circuits with high logic densities and reduced depths. Experimental results indicate a significant improvement in performance over traditional realizations. An important property of technologydependent optimizations is the simultaneous improvement in all the performance parameters. This is in contrast to the technology-independent optimizations where there is always an application driven trade-off between different performance parameters.

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“…Proposed Christoffel-Darboux formula for four orthogonal polynomials on two equal finite intervals for powerfully generating filter functions is proposed. In [13] is described in detail the analytical method for the synthesis of the multiplierless linearphase 1D and 2D FIR filter functions in an explicit form using Chebyshev orthogonal polynomials of the first kind. In [14] is described an analytical method for the synthesis of the multiplierless linear-phase 2D FIR filter functions in a compact form that can have the effect of Hilbert transformer in the z 2 domain.…”

Section: Introductionmentioning

confidence: 99%

A novel analytical method for the selective multiplierless linear-phase 2D FIR filter function

Djordjevic-Kozarov

Pavlović

2016

FACTA U EE

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In this paper, a novel analytical method for new class of selective linear-phase two-dimensional (2D) finite impulse response (FIR) filter functions generated by applying a new modified 2D Christoffel-Darboux formula for classical orthogonal Chebyshev polynomials of the first and the second kind is proposed. Fundamental research proposed in this paper is also illustrated by examples of 2D FIR filter and adequate comparison with new class of multiplierless linear-phase 2D FIR filter function given in the literature.

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1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind

Cited by 30 publications

References 25 publications

Shape of impulse response characteristics of linear-phase nonrecursive 2D FIR filter function

Shape of impulse response characteristics of linear-phase nonrecursive 2D FIR filter function

Technology - Dependent Optimization of FIR Filters based on Carry - Save Multiplier and 4:2 Compressor unit

A novel analytical method for the selective multiplierless linear-phase 2D FIR filter function

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