Low-Complexity 2-D Digital FIR Filters Using Polyphase Decomposition and Farrow Structure
Abstract : This paper proposes a novel realization technique for quadrantally symmetric 2-D finite impulse response filters with a guaranteed reduction in the hardware complexity. Here, the concept of Farrow structure-based interpolation filter design using the polyphase decomposition of the 1-D filter transfer function is effectively utilized in the 2-D domain. The proposed 2-D filter makes use of row-wise polyphase decomposition of the 2-D transfer function or frequency response, followed by the polynomial approximation of the individual polyphase coefficients resulting in Farrow structures corresponding to each row filter. The final coefficients are implemented by varying the delay values in all the Farrow structures, followed by the interpolation of the coefficients obtained from each delay value, which in turn forms the rows in the 2-D kernel. The major highlight of the proposed method is the highly reduced implementation complexity in terms of the number of multipliers and adders, with a low normalized root-mean-square error. Design examples of the circularly symmetric and fan-type filters have been considered to show the efficiency of the approach. The results show a drastic reduction in the implementation complexity of the 2-D filters of upto 20%, with significantly low normalized root-mean-square error lesser than 0.5%.
? It can also be designed using frequency-domain optimization, as in most of the existing design methods.
? The novelty of the presented lattice structure is that it not only inherits the desirable attributes of 1- D Gray-Markel lattice all pass structure but also possesses the advantage of better performance over the existing 2-D lattice all pass structures.
? A Sequential Partial Optimization Algorithm for Minimax Design of Separable- Denominator 2-D IIR Filters is proposed in paper.
? A new algorithm is proposed to synthesize finite-precision coefficients with low implementation cost from the frequency response specifications of linear phase FIR filter.
? The disadvantage is that, due to the switching between the different structures, the implementation becomes more complex if one wants to avoid transient problems.
? In this way, the number of optimization problems that needs to be solved is limited to a rather small number.
? The analog filter bank is not easy to be implemented, a digital filter bank method is proposed to solve the reconstruction problem.
? An optimization problem is formulated that minimizes the complexity measure of the narrow transition band FIR filter under the constraints of length of the filter and normalized peak ripple magnitude (NPRM) threshold.
• This paper proposes a totally multiplier-less farrow structure based linear phase low-pass interpolation filter.
• In this paper, the low pass filter structure proposed is made multiplier-less in order to reduce the implementation complexity further.
• In this proposed scheme, the approximation error in the frequency response of the CSD rounded filter with respect to that with the continuous coefficients, is to be minimized.
• A multimodal FIR filter design using opposition based harmony search algorithm is proposed in paper and compared with other filters designed using PM, RGA, PSO and DE.
? The coefficients obtained from each Farrow structure using the different fractional delays are suitably interpolated to realize the individual rows in the 2D kernel.
? Farrow structure based interpolation filter design approach has been reported to be an efficient low complexity method for the implementation of higher order 1D FIR interpolation filters.
? The coefficients of the different polynomials form the different sub-filter coefficients of the Farrow structure.
? The transformation based approach is a flexible design approach, where the 2D filter coefficients in the frequency domain are directly obtained from their 1D impulse response coefficients by applying a frequency transformation.
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