2017
DOI: 10.1007/s00034-017-0618-2
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Synthesis and Realization of 3-D Orthogonal FIR Filters Using Pipeline Structures

Abstract: The authors present a novel design algorithm for 3-D orthogonal filters. Both separable and non-separable cases are discussed. In the separable case, the synthesis leads to a cascade connection of 1-D systems. In the latter case, one obtains 2-D systems followed by a 1-D one. Realization techniques for these systems are presented which utilize Givens rotations and delay elements. The results are illustrated by examples of separable and non-separable 3-D system designs, i.e., Gaussian and Laplacian filters.

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Cited by 6 publications
(10 citation statements)
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“…An implementation utilizing the CORDIC algorithm, among others, is presented in [11,12] and [13]. In papers [14][15][16], possible implementations of orthogonal 3-D FIR filters have been described.…”
Section: Gx Y =mentioning
confidence: 99%
See 1 more Smart Citation
“…An implementation utilizing the CORDIC algorithm, among others, is presented in [11,12] and [13]. In papers [14][15][16], possible implementations of orthogonal 3-D FIR filters have been described.…”
Section: Gx Y =mentioning
confidence: 99%
“…implementation method of the system based on Givens rotations. The author's research on the obtainment of 3-D rotation systems was presented in a consistent series of publications [14][15][16] and [17][18][19]. The methods presented there were based on the utilization of the properties of the transfer function with three variables.…”
mentioning
confidence: 99%
“…This approach can be used to obtain a pipelined rotation structure [11,16,17] easily. To synthesise the 3D digital system, the state-space approach has been chosen because it provides an opportunity to adopt 1D methods to higher dimension (2D, 3D, and nD) solutions [17]. Furthermore, the state-space lossless orthogonal structures achieve good performance under finite arithmetic.…”
Section: Synthesis Algorithmmentioning
confidence: 99%
“…Since the first pulse-code modulation transmission of digitally quantized speech, in World War II, digital signal processing (DSP) began to proliferate to all areas of human life. Classical digital systems are known to possess poor parameters under finite-precision arithmetic, like frequency response sensitivity to changes in the structural parameters, noise, inner oscillations, and limit cycles [14]. These effects have led to development of wave filters [15] and orthogonal filters.…”
Section: Introductionmentioning
confidence: 99%
“…For example, in [18], the development of the pipelined structure of digital orthogonal filters started. It continued in the 1990's till present days [14]. When the two most common approaches are compared, state-space realization has advantages in the case of MIMO filters; it provides a better insight into their structure.…”
Section: Introductionmentioning
confidence: 99%