Description

Low-Complexity 2-D Digital FIR Filters Using Polyphase Decomposition and Farrow Structure

Existing System:

THE design and implementation of 2-D filters is a crucial area, widely explored by researchers due to the wide variety of applications they offer. The application areas include pattern recognition systems, computer image processing, seismic signal processing, biomedical systems, and genomic signal processing. Since many critical applications such as real-time medical image analysis, require fast 2-D filtering operations with filter kernels of large size, effective, fast, low complexity and low power implementation approaches for 2D filters, become essential.

Among the different design approaches for 2D filters, the transformation based approach is a widely used design method for circular and fan-type filters. In the transformation-based method, a suitable 1D filter is designed first, followed by mapping the 1D filter coefficients to 2D domain using specific transformation kernels. McClellan transformation was the first transformation introduced for designing circular 2D filters from their 1D counterparts. In, two new multiplierless transformations were introduced, which was a remarkable achievement over McClellan transformation, towards the aim of designing circular 2D filters of improved circularity. Later, with an aim of designing 2D filters of lower implementation complexity and improved circularity, a new P2 transformaton was proposed. The McClellan transformation based design approach was also extended for the design of fan filters in and, where the transformation coefficients were deduced using different optimization algorithms by maintaining a minimum contour deviation error. Bindima et al. have deduced the transformation coefficients for fan-type filters using multi objective artificial bee colony optimization by ensuring the least contour deviation error.

The 2D filter designed using the transformation method has an efficient implementation structure based on Chebyshev recursion formula, which consists of cascaded 2D transformation kernels F(z1,z2), where F(z1,z2) represents the 2D transformation function corresponding to the spectral transformation F(ω1, ω2) used. But the Chebyshev structure based implementation in the z domain has a major disadvantage of increased delay due to the use of cascaded 2D kernels F(z1,z2), which in turn act as a limitation to the high speed filtering. The implementation of a 2D filter of size (2N +1)×(2N+1) requires a cascade of N number of similar F(z1,z2) blocks. This, in turn, introduces an overall delay of z−N 1 z−N 2 for the transformation-based realizations. Moreover, the realization of the transformations such as P2 that provide better contour circularity requires fractional delay filters to realize z−1 2 . An alternative solution to overcome the delays involved in the 2D filter realization is to use the Chebyshev structure for frequency domain-based implementation of the 2D filter. But the realization of the 2D filter in the frequency domain requires larger number of multipliers and thus increases the implementation complexity.

Apart from transformation-based methods, different optimization based methods were also introduced for the design of 2D filters, where the entire (2N + 1) × (2N + 1) number of 2D filter coefficients for specific contours, are obtained by minimizing the contour deviation error. The realization of these 2D filters relies upon the direct form implementation of the 2D transfer function. Thus, the realization of a 2D filter of size equal to (2N + 1) × (2N + 1) requires 2N delays both in the z1 and z2 space. On the other hand, the frequency domain realization of the filters increases the implementation complexity. Recently, a computationally efficient 2D filter design approach using sampling-kernel based interpolation and frequency transformation is proposed for the design of sharp 2D FIR filters [13], which focusses on reducing the implementation complexity of the 2D filters. The major drawback of this approach is the design complexity in yielding the optimal lengths of the different sub-filters.

This paper proposes a novel implementation structure for 2D filters of reduced hardware complexity in frequency domain. The proposed implementation structure makes use of the theory of the design of interpolation filters using 1D Farrow structure. The proposed implementation structure realizes the polyphase components corresponding to each row in the filter kernel using the Farrow structure, and the overall 2D filter is realized using a set of parallel Farrow structures, all tunable with the same fixed set of fractional delays. The coefficients obtained from each Farrow structure using the different fractional delays are suitably interpolated to realize the individual rows in the 2D kernel. The total delay involved in the realization of the individual row filters reduces to K, where K represents the order of each polyphase subfilter. The proposed low complexity implementation of the 2D filter has been demonstrated for circular 2D filters and fan-type filters, and can be extended to other types such as elliptical and diamond filters. The quadrantal symmetry of the 2D circular and fan-type filter kernels, which are designed using the existing transformation based approaches, ensure the filter coefficients h(n1, n2) to satisfy the condition h(n1, n2) = h(N − n1, n2) = h(n1, N − n2) for a 2D filter of order equal to N×N. This can also be effectively utilized in reducing the hardware complexity. The proposed method offers effective hardware implementation and better complexity reduction than the state of art methods.

Disadvantages:

• • More complexity in Crucial area
  • More power dissipation
  • More delay

Proposed System:

In this recent digital signal processing applications, will have lot of filter designs in finite impulse response method, in such as it will take more complexity in 2D domain thus it will take more hardware complexity in crucial area and more critical paths, here this proposed work will presents a Farrow structure based interpolation filter design using the polyphase decomposition of 1D filter which effectively utilized in 2D digital domain, here this polyphase decomposition and Farrow structure will implemented using truncation multiplier, this truncation method will reduced the hardware complexity in internal and external part of multiplication and additions, thus it will provide n x n of n output in all sub filters. Finally this work presents in VHDL and synthesized in XILINX FPGA, and compared in terms of area, delay and power.

Advantages:

• More complexity in Crucial area
• More power dissipation
• More delay

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Low-Complexity 2-D Digital FIR Filters Using Polyphase Decomposition and Farrow Structure

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