Implementation Of Two-dimensional Digital Filters Research Articles

Implementation of real coefficient two-dimensional denominator-separable digital filters based on decomposition techniques

In the paper, the implementation of two-dimensional digital filters is dealt with for the processing of real sequences. The approach is based on decomposition techniques to obtain separable one-dimensional polynomials from a two-dimensional polynomial, and then one-dimensional techniques are used to express the one-dimensional transfer functions as a sum of two reduced-order transfer functions with complex coefficients. Thus, new realisation structures are obtained for the equivalent reduced-order complex-coefficient transfer functions for the processing of real sequences. The authors concentrate more on two-dimensional denominator-separable digital filters and also confine themselves to the parallel-form structures as the emphasis is now on low data throughput delay and high parallelism due to recent advances in VLSI technology. All these structures consist only of one-dimensional first-order minimum-norm sections. Thus, these structures possess low round-off noise and freedom from overflow limit cycles. A comparison of different structures is made based on data throughput delay, efficiency in multiprocessor environment and round-off noise properties.

Minimum cycle fast implementation of two-dimensional digital filters based on the LU decomposition

A new architecture for two-dimensional filters is presented, which is based on the LU matrix decomposition and is characterized by minimum cycle time. The clock cycle time in the proposed structure is determined by one multiplication and three additions, which are the maximum number of arithmetic operations in the critical path, independently of the filter's order. This realization is characterized by all known advantages of decomposition structures (modularity, parallelism, reconfigurability) and may be used in real-time image processing applications.

Block decomposition structures for the fast modular implementation of two-dimensional digital filters

A general structure is presented for the block realization of two-dimensional infinite impulse response digital filters, which is based on the two-dimensional matrix convolution equations and the decomposition of their associated transfer function matrices. The proposed decomposition may be considered as an extension of the scalar decomposition technique, which has already been used for the realization of two-dimensional digital filters associated with two-variable polynomials. The decomposition structure is considered in two different forms, which correspond to the direct forms I and II. It is shown that if a given two-dimensional single-input, single-output filter is realizable, then realizable block decomposition structures may be always selected. The proposed approach is general and applies without any restriction for the block implementation of any two-dimensional filter. The resulting structures are characterized by high inherent parallelism, modularity, regularity, reconfigurability, local interconnections, and very high sampling and throughput rates. Thus they are well suited for VLSI implementation and implementation via multiprocessor systems and array processors, such as systolic and wavefront arrays.

Real-time image processing by distributed arithmetic implementation of two-dimensional digital filters

This paper describes the implementation of two-dimensional recursive digital filters for real-time image processing. The filter structure is described by distributed arithmetic and the operations involved are memory fetches and additions. An error analysis of the two-dimensional filter structure described by distributed arithmetic is outlined and the expression for the mean-squared error is derived. This approach is compared to an equivalent conventional filter structure using multipliers. It is demonstrated that the distributed arithmetic implementation offers a significant reduction in cost as well as power consumption for real-time image processing. In addition, the hardware design of a second-order two-dimensional distributed filter is presented and its performance is examined. This filter is constructed using standard integrated circuits and memories and is capable of filtering images of sizes up to 256 × 256 pixels in real time.

Block implementation of two-dimensional digital filters

A novel principle known as block transformation is developed for the block implementation of two-dimensional (2-D) digital filters. It employs the one-dimensional (1-D) block implementation concept forwarded by Burrus ( 7) as a basic tool. Using this block transformation principle three distinct forms of 2-D block equations are derived. The generalized nature of the approach presented here facilitates the straightforward extension of this technique to higher dimensional digital filters.