Hari C. Reddy

Symmetry Study for Delta- Operator-Based 2-D Digital Filters

The complexity in the design and implementation of two-dimensional (2-D) filters can be considerably reduced if we utilize the symmetries that might be present in the frequency response of these filters. As the delta-operator formulation of digital filters offers better numerical accuracy and lower coefficient sensitivity in narrowband 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 filter specifications. With this motivation, we comprehensively establish the theory of constraints for delta-operator formulated discrete-time real-coefficient polynomials and functions, arising out of the many types of symmetries in their magnitude responses. We also show that as sampling time tends to zero, the gamma-domain symmetry constraints merge with those of s-domain symmetry constraints. We then present a least square error criterion based procedure to design 2-D digital filters in gamma-domain that utilizes the symmetry properties of the magnitude specification. A design example is provided to illustrate the savings in computational complexity resulting from the use of the gamma-domain symmetry constraints

Symmetry study on 2-D complex analog and digital filter functions

The symmetry properties of 2-D complex polynomials are analyzed in this paper. The characteristics of a polynomial possessing different standard symmetries in their magnitude and phase responses are studied. The nature of constraints that are imposed by the defined symmetries on analog and digital polynomials is discussed. The various classes of complex polynomials possessing the different (quadrantal, diagonal, rotational, and octagonal) symmetries and antisymmetries in their magnitude responses and/or phase responses are tabulated.

Power-Efficient and Cost-Effective 2-D Symmetry Filter Architectures

This paper presents two-dimensional (2-D) VLSI digital filter structures possessing various symmetries in the filter magnitude response. For this purpose, four Type-1 and four Type-2 power-efficient and cost-effective 2-D magnitude symmetry filter architectures possessing diagonal, fourfold rotational, quadrantal, and octagonal symmetries with reduced number of multipliers and one power-efficient and cost-effective multimode 2-D symmetry filter are given. By combining the identities of the four Type-1 symmetry filter structures, the proposed multimode 2-D symmetry filter is capable of providing four different operation modes: diagonal symmetry mode (DSM), fourfold rotational symmetry mode (FRSM), quadrantal symmetry mode (QSM), and octagonal symmetry mode (OSM). The proposed diagonal, fourfold rotational, quadrantal, and octagonal symmetry filter structures can attain power savings of 16.77%, 36.30%, 22.90%, and 37.73% with respect to that of the conventional 2-D filter design without symmetry. On the other hand, the proposed DSM, FRSM, QSM, and OSM modes can reduce power consumption by 11.01%, 31.42%, 17.53%, and 35.26% compared with that of the conventional 2-D filter design. The proposed multimode filter can result in a 63.25% area reduction compared with the sum of the areas of the four individual Type-1 symmetry filter structures.

2-D digital filter architectures without global broadcast and some symmetry applications

Four new 2-D filter VLSI architectures without global broadcast are presented. The first is a transposed systolic structure which requires fewer delay elements compared to the original systolic structure in [1]. By combining the sub-blocks of the original with the new transposed structure, two additional systolic structures are obtained to realize transfer functions with separable denominators, which require fewer multipliers. These separable denominator structures have important symmetry applications. A structure which possesses diagonal symmetry is then shown which requires even fewer multipliers.

Generalized formulation of 2-D filter structures without global broadcast for VLSI implementation

A generalized formulation is developed that allows the derivation of various new 2-D VLSI filter structures, without global broadcast, using different filter sub-blocks and their interconnections (frameworks). With this formulation, lattice-type and direct-form structures realizing general 2-D IIR and FIR transfer functions, IIR transfer functions with separable denominators, and transfer functions with quadrantal magnitude symmetry are easily obtained. The separable denominator and quadrantal symmetry structures have the advantage of reduced number of multipliers.

Theory and test procedure for symmetries in the frequency response of complex two-dimensional delta operator formulated discrete-time systems

This paper provides the theory and an efficient tabular algorithm to test for various symmetries in the magnitude response of two-dimensional (2-D) complex-coefficient delta operator formulated discrete-time systems. In general, centro symmetry is not preserved in the complex case. The conditions under which this is preserved is discussed in the paper. It is to be noted that as the sampling period (/spl Delta/) goes to zero, the symmetry conditions merge with that of 2-D continuous-time case.

Study of various symmetries in the frequency response of two-dimensional delta operator formulated discrete-time systems

This paper deals with the definitions and the testing for the presence of various symmetries in the magnitude response of two-dimensional (2-D) delta operator formulated discrete-time systems. The symmetry constraints defined provide a unification with the analog 2-D case. With the sampling period=0, the results correspond to the conditions on analog polynomial magnitude symmetry.

A new VLSI 2-D diagonal-symmetry filter architecture design

In this paper, we propose two new two-dimensional (2-D) IIR and FIR filter architectures for 2-D transfer function with diagonal symmetry. The presented type-I structure with diagonal symmetry has the lowest number of multipliers, and zero latency without sacrificing the number of the delay elements. Importantly, the proposed type-II IIR filter possesses high speed, local broadcast, and the same number of multipliers and latency as the type I shows at expense of a slight increment of number of delay elements.

Delta operator based 2-D filter design using symmetry constraints

This paper presents an optimization-based 2-D filter design procedure that utilizes the recently derived symmetry constraints in gamma domain. The gamma domain transfer function has significant coefficient sensitivity advantage compared to the same procedure applied to the conventional q-operator based design with the same symmetry constraints.

A new VLSI 2-D fourfold-rotational-symmetry filter architecture design

In this paper, we propose two new two-dimensional (2-D) IIR and FIR filter architectures for 2-D transfer function using fourfold rotational symmetry. The presented type-I structure with fourfold rotational symmetry has the lowest number of multipliers, and zero latency. Importantly, the proposed type-II IIR filter possesses high speed, local broadcast, and the same number of multipliers and latency as the type I shows at expense of a slight increment of number of delay elements.