Browsing by Author "Khoo, I. -Hung"

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General formulation of shift and delta operator based 2-D VLSI filter structures without global broadcast and incorporation of the symmetry
(2014-10-01)
Khoo, I. -Hung
;
Reddy, Hari C.
;
Van, Lan-Da
;
Lin, Chin-Teng
;
資訊工程學系
Having local data communication (without global broadcast of signals) among the elements is important in very large scale integration (VLSI) designs. Recently, 2-D systolic digital filter architectures were presented which eliminated the global broadcast of the input and output signals. In this paper a generalized formulation is presented that allows the derivation of various new 2-D VLSI filter structures, without global broadcast, using different 1-D filter sub-blocks and different interconnecting frameworks. The 1-D sub-blocks in z-domain are represented by general digital two-pair networks which consist of direct-form or lattice-type FIR filters in one of the frequency variables. Then, by applying the sub-blocks in various frameworks, 2-D structures realizing different transfer functions are easily obtained. As delta discrete-time operator based 1-D and 2-D digital filters (in gamma-domain) were shown to offer better numerical accuracy and lower coefficient sensitivity in narrow-band filter designs when compared to the traditional shift-operator formulation we have covered both the conventional z-domain filters as well as delta discrete-time operator based filters. Structures realizing general 2-D IIR (both z- and gamma-domains) and FIR transfer functions (z-domain only) are presented. As symmetry in the frequency response reduces the complexity of the design, IIR transfer functions with separable denominators, and transfer functions with quadrantal magnitude symmetry are also presented. The separable denominator frameworks are needed for quadrantal symmetry structures to guarantee BIBO stability and thus presented for both the operators. Some limitations of having exact symmetry with separable 1-D denominator factors are also discussed.
Unified theory of symmetry for two-dimensional complex polynomials using delta discrete-time operator
(2011-03-01)
Khoo, I. -Hung
;
Reddy, Hari C.
;
Rajan, P. K.
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資訊學院
;
College of Computer Science
The complexity in the design and implementation of 2-D filters can be reduced considerably if the symmetries that might be present in the frequency responses of these filters are utilized. As the delta operator (gamma-domain) formulation of digital filters offers better numerical accuracy and lower coefficient sensitivity in narrow-band filter designs when compared to the traditional shift-operator formulation, it is desirable to have efficient design and implementation techniques in gamma-domain which utilize the various symmetries in the filter specifications. Furthermore, with the delta operator formulation, the discrete-time systems and results converge to their continuous-time counterparts as the sampling periods tend to zero. So a unifying theory can be established for both discrete- and continuous-time systems using the delta operator approach. With these motivations, we comprehensively establish the unifying symmetry theory for delta-operator formulated discrete-time complex-coefficient 2-D polynomials and functions, arising out of the many types of symmetries in their magnitude responses. The derived symmetry results merge with the s-domain results when the sampling periods tend to zero, and are more general than the real-coefficient results presented earlier. An example is provided to illustrate the use of the symmetry constraints in the design of a 2-D IIR filter with complex coefficients. For the narrow-band filter in the example, it can be seen that the gamma-domain transfer function possesses better sensitivity to coefficient rounding than the z-domain counterpart.