2D Finite Impulse Response Filters Research Articles

Higher order and optimized symmetric 2D FIR filter design and hardware architecture implementation using CSD-CSE

In this paper, an optimized and high-performance Two-Dimensional (2D) Finite Impulse Response (FIR) filter is designed and hardware architecture is implemented for image processing applications. The higher-order circular symmetric 2D FIR filter is designed using a modified McClellan Transformation called a P4 transformation. The perfect circular symmetry in the contour of the 2D FIR filter and less complexity and error are attained by this proposed P4 Transformation. Next, the designed filter coefficients are represented by the Canonical Signed Digit (CSD) number format to attain the multiplier-less design to avoid the power complexity multipliers. Further, to reduce the hardware complexity, the Common Subexpression Elimination (CSE) technique is utilized to reduce the number of adders and hence area and power are decreased. Each sub-filter corresponding to the CSD coefficient rows is realized and integrated as a 2D FIR filter using a Fully Direct-type architecture. This 2D FIR filter architecture is coded by Verilog and synthesized by Cadence tools in a 45 nm CMOS technology library. The Delay, Power Consumption (PC), and Area reports were generated by the Genus synthesis tool and compared with the state-of-the-art works. The PC, area, and delay of the proposed filter architecture are reduced to the minimum of 13.96%, 69.1%, and 1.4%, respectively when compared to the existing filter architectures. The maximum of 10.48 times and a minimum of 1.18 times of Area Delay Product (ADP), and a maximum of 10.69 times and a minimum of 1.063 times of Power Delay Product (PDP) are smaller than the existing 2D filter architectures.

Area-Delay-Power Efficient VLSI Architecture 2D FIR Filter using Modified Multipliers and Adders

In this paper, a low power, area, and delay 2D Finite Impulse Response (FIR) filter architecture is derived from an analysis of a memory-efficient design. The completely direct-form 2D FIR filter is where the idea of parallel processing is first presented. As a result, the FIR filter may make better use of its memory by reusing its contents. With a block size of L and a filter length of N, a non-separable 2D FIR filter structure is developed and implemented. The FIR filter's arithmetic module makes use of high-speed, low-power multipliers and Carry Look Ahead (CLA) adders, with the output calculated by a pipelined adder unit. Verilog HDL code is used to represent the proposed architecture, and the CADENCE environment's NC Simulator and RTL Compiler synthesis tool are used to verify the design. Existing memory-efficient 2D FIR filter hardware architectures are compared to the produced area, power, and delay reports. Using Modified CLA (MCLA) adders and pipelining, we were able to cut down on power consumption by 44% and delay by 20%. Index Terms: Memory reuse, 2D-FIR filter, Low Power Multiplier, Parallel Prefix Adder, Carry Look Ahead adder, and pipelining.

Implementation of block-based diagonal and quadrantal symmetry type 2D-FIR filter architectures using DA technique

The efficient architectures of Two-Dimensional (2D) Finite Impulse Response (FIR) filters are proposed for image processing applications. The performance metrics such as power consumption, area, and delay of the architectures can be optimized using VLSI design. The 2D FIR filter architectures can be implemented using parallel or block processing to increase the filter throughput and to prune the number of clock cycles required for image processing. The symmetry in the filter coefficients decreases the number of multipliers, whereas the multiplier block is very complex and a power-consuming block in the filter architecture. In this work, two types of symmetric architectures such as diagonal symmetry and quadrantal symmetry filters are proposed. The remaining multipliers required for the filter architecture are replaced by Distributed Arithmetic (DA) logic. The memory-based DA reduces the LUT size and hence the area, power, and delay are reduced in the filter architecture. Block processing, symmetry, and DA concepts are introduced here to optimize the 2D FIR filter architecture. The proposed architectures are implemented in 45 nm CMOS technology using Cadence Genus Synthesis tools and area, delay, power, Area-Delay Product (ADP), and Power-Delay Product (PDP) results are obtained and compared with state-of-the-art works. The ADP value of the proposed diagonal symmetry architecture is decreased by a maximum of 73.34 %, and a minimum of 20.39 %, and the PDP value is decreased by a maximum of 90.28 %, and a minimum of 21.27 % when compared to the existing works. The ADP and PDP values of the proposed quadrantal symmetry are decreased by a minimum of 23.62 %, and 27.74 % when compared to existing works, respectively.

Development of variable 2D FIR filter structures using farrow approximation and row-wise polyphase decomposition

This work proposes pre and post Farrow approximation of row-wise polyphase decomposed 2D finite impulse response (FIR) filters to achieve variability in 2D bandwidths with low implementation costs. The proposed method starts with realizing variable 2D filters using the 2D Farrow structure. The 2D Farrow filter structure is then row-wise polyphase decomposed and approximated in terms of fractional delay again to obtain the final set of coefficients. To illustrate the efficiency of the proposed methodology, design examples of variable circular and elliptical filters are provided in this paper. The simulation results show that the proposed methodology can result in variable 2D FIR filters with a considerable reduction in the number of multipliers w.r.t the existing approaches without much degradation in the performance parameters.

A novel filter-bank architecture of 2D-FIR symmetry filters using LUT based multipliers

In this paper, a novel block-based generic filter bank architecture is proposed for various Two Dimensional (2D) symmetry Finite Impulse Response (FIR) filers. It is implemented to prune the area, storage memory, and power consumption of the filter bank. Four 2D symmetrical FIR filter architectures are implemented and explored along with a general filter (without symmetry). The symmetry in coefficients of the filter reduces the number of multiplier blocks (most power-hunger blocks) required for the structure. Hence, a major part of the total power consumption is decreased. Block processing is introduced to improve the throughput of the filter bank. The memory sharing and memory reuse concepts are incorporated to reduce the storage memory of the entire filter bank. Finally, the conventional multiplication process is replaced with memory-based dual-port Look-Up-Table (LUT)-Distributed Arithmetic (DA) multipliers to minimize the power and area of each sub-filter of the filter bank. A generic filter bank architecture is implemented and synthesized in CMOS 45 nm generic library using Genus tools and physical design is carried out by Innovus tools from Cadence. The final layout of the design is generated using proper floor planning, placement, and routing in physical design. The results are compared with the state-of-art works of 2D FIR filters. The significantly improved results are reported in terms of area, power, delay, and memory.

Design and implementation of low complexity circularly symmetric 2D FIR filter architectures

This paper presents a low complexity two dimensional (2D) circular symmetric Finite Impulse Response (FIR) filter design and implementation of architecture. The optimized circular symmetric 2D FIR filter is designed using a modified Park–McClellan transformation method and filter coefficients are quantized using a canonical signed digit (CSD) binary number format. The CSD encoded coefficients are optimized to reduce the number of adder/subtractors using common subexpression elimination (CSE) algorithms. Based on the modified filter coefficients, the two structures fully direct form and hybrid-II form 2D FIR filter architectures are implemented using CSD and CSD with Horizontal CSE and Vertical CSE techniques. The proposed architectures compared with the conventional symmetry 2D filters and state-of-the-art architectures in terms of area, power, and speed.

Two dimensional cuckoo search optimization algorithm based despeckling filter for the real ultrasound images

A clinical ultrasound imaging plays a significant role in the proper diagnosis of patients because, it is a cost-effective and non-invasive technique in comparison with other methods. The speckle noise contamination caused by ultrasound images during the acquisition process degrades its visual quality, which makes the diagnosis task difficult for physicians. Hence, to improve their visual quality, despeckling filters are commonly used for processing of such images. However, several disadvantages of existing despeckling filters discourage the use of existing despeckling filters to reduce the effect of speckle noise. In this paper, two dimensional cuckoo search optimization algorithm based despeckling filter is proposed for avoiding limitations of various existing despeckling filters. Proposed despeckling filter is developed by combining fast non-local means filter and 2D finite impulse response (FIR) filter with cuckoo search optimization algorithm. In the proposed despeckling filter, the coefficients of 2D FIR filter are optimized by using the cuckoo search optimization algorithm. The quantitative results comparison between the proposed despeckling filter and other existing despeckling filters are analyzed by evaluating PSNR, MSE, MAE, and SSIM values for different real ultrasound images. Results reveal that the visual quality obtained by the proposed despeckling filter is better than other existing despeckling filters. The numerical results also reveal that the proposed despeckling filter is highly effective for despeckling the clinical ultrasound images.

Texture analysis using complex wavelet decomposition for knee osteoarthritis detection: Data from the osteoarthritis initiative

The classification of subjects with different stages of knee OsteoArthritis (OA) using bone texture analysis is a challenging task in medical imaging. This paper presents a new approach for texture analysis of radiographic OA in knee X-ray images. First, a preprocessing step based on a 2D finite impulse response filter is applied on the X-ray images. Then, a set of image content descriptors is extracted from the complex wavelet decomposition using different statistics of a new concept of the relative phases of complex coefficients. The Von Mises and wrapped Cauchy probability density functions are used to model the distribution of relative phase coefficients. Finally, the estimated parameters for each image are used in the classification task, to verify the effectiveness and robustness of the proposed texture analysis on knee X-ray images from the OsteoArthritis Initiative (OAI). Results show that the proposed approach leads to improved texture analysis with a classification rate of 80.38%.

An iterative technique for optimally designing a separable 2D FIR filter

The optimal design of a separable two‐dimensional (2D) finite impulse response (FIR) filter is a nonlinear programming problem. In this paper, an iterative alternating optimization technique for optimally designing the separable 2D FIR filter in the mini‐max sense and the least‐square sense is proposed. Implementation of the proposed technique only requires a suitable initial solution. The simulation experiment validates the effectiveness of the proposed technique. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Fast super-resolution algorithm using rotation-invariant ELBP classifier and hierarchical pattern matching

This paper proposes a fast super-resolution (SR) algorithm using content-adaptive two-dimensional (2D) finite impulse response (FIR) filters based on a rotation-invariant classifier. The proposed algorithm consists of a learning stage and an inference stage. In the learning stage, we cluster a sufficient number of low-resolution (LR) and high-resolution (HR) patch pairs into a specific number of groups using the rotation-invariant classifier, and choose a specific number of dominant clusters. Then, we compute the optimal 2D FIR filter(s) to synthesize a high-quality HR patch from an LR patch per cluster, and finally store the patch-adaptive 2D FIR filters in a dictionary. Also, we present a smart hierarchical addressing method for effective dictionary exploration in the inference stage. In the inference stage, the ELBP of each input LR patch is extracted in the same way as the learning stage, and the best matched FIR filter(s) to the input LR patch is found from the dictionary by the hierarchical addressing. Finally, we synthesize the HR patch by using the optimal 2D FIR filter. The experimental results show that the proposed algorithm produces better HR images than the existing SR methods, while providing fast running time.

Low power 2D finite impulse response filter design using modified artificial bee colony algorithm with experimental validation using field‐programmable gate array

Motivated by the need of reducing power consumption (PC) in two dimensional (2D) finite impulse response (FIR) filters, in this work, the 2D FIR filter design task is formulated as an optimisation problem that seeks to attain the desired frequency response and reduces PC. The optimisation problem has been solved using the modified version of artificial bee colony algorithm. The applicability of the proposed approach has been evaluated by designing circular shaped 2D FIR filters for a set of specifications in frequency domain. The designed filters have been compared with other reported state of the art techniques. The evaluation is carried out in terms of pass band and stop band ripple minimisation, convergence profile and PC during filter execution in hardware. The proposed technique is found to outperform all other techniques in achieving minimum ripple for a given filter order. To prove the effectiveness of the proposed approach for PC reduction, the designed filters have been implemented in hardware using field-programmable gate array (xc7vx485t-2ffg1761). The PC computed using Xilinx X-power analyser shows that 23.53% power can be saved using the proposed approach as compared with conventional design approaches.

A novel analytical method for the selective multiplierless linear-phase 2D FIR filter function

In this paper, a novel analytical method for new class of selective linear-phase two-dimensional (2D) finite impulse response (FIR) filter functions generated by applying a new modified 2D Christoffel-Darboux formula for classical orthogonal Chebyshev polynomials of the first and the second kind is proposed. Fundamental research proposed in this paper is also illustrated by examples of 2D FIR filter and adequate comparison with new class of multiplierless linear-phase 2D FIR filter function given in the literature.

Design of computationally efficient 2D FIR filters using sampling‐kernel‐based interpolation and frequency transformation

A closed-form design of a two-dimensional (2D) finite impulse response (FIR) filter with circular, rectangular, fan or quadrant-fan shapes in the passband region is presented. The computationally efficient 2D FIR filter can be implemented using frequency transformation and sampling-kernel-based interpolation instead of an optimisation algorithm. When compared with the existing method, the proposed method reduces 90% of multiplications for filtering. Several design examples are demonstrated to verify the performance of the proposed design.

Ultra‐selective spike multiplierless linear‐phase two‐dimensional FIR filter function with full Hilbert transform effect

In this study, a novel analytical method for new class of linear-phase two-dimensional (2D) finite impulse response (FIR) filter functions with full effect of Hilbert transformer in z 1 and z 2 domains generated by applying a new modified 2D Christoffel–Darboux formula for classical orthogonal Chebyshev polynomials of the first and the second kind is proposed. Fundamental research proposed in this study is also illustrated by examples of 2D FIR filter, Hilbert transformer and adequate comparison with new class of multiplierless linear-phase 2D FIR filter function given in the literature. For all 2D FIR filter functions, comparisons are made for the same values of free real parameters, and they show the improvement of the spike sharpness.

Subpixel‐based image downsampling algorithm using content‐adaptive two‐dimensional FIR filters

This study proposes a subpixel-based image downsampling algorithm using content-adaptive two-dimensional (2D) finite impulse response (FIR) filters. The proposed algorithm consists of a learning stage and an inference stage. In the learning stage, using a sufficient number of low-resolution (LR) and high-resolution (HR) patch pairs, the authors compute optimal 2D FIR filters to synthesise LR patches of the highest quality from a specific HR patch and store the patch-adaptive 2D FIR filters in a dictionary. In the inference stage, they explore candidates that best match to each HR input patch in the dictionary and synthesise LR patches by using their corresponding 2D FIR filters on a subpixel basis. The experimental results show that the proposed algorithm produces higher-quality LR images on a patch basis than existing methods and entails no blur and aliasing artefacts.

Implementation of 2D explicit depth extrapolation FIR digital filters for 3D seismic volumes using singular value decomposition

We propose a new scheme for implementing predesigned 2D complex-valued wavefield extrapolation finite impulse response (FIR) digital filters, which are used for extrapolating 3D seismic wavefields. The implementation is based on singular value decomposition (SVD) of quadrantally symmetric 2D FIR filters (extrapolators). To simplify the SVD computations for such a filter impulse response structure, we apply a special matrix transformation on the extrapolation FIR filter impulse responses where we guarantee the retention of their wavenumber phase response. Unlike the existing 2D FIR filter implementation methods that are used for this geophysical application such as the McClellan transformation or its improved version, this implementation via SVD results in perfect circularly symmetrical magnitude and phase wavenumber responses. In this paper, we also demonstrate that the SVD method can save (depending on the filter size) more than 23% of the number of multiplications per output sample and approximately 62% of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2D convolution. Finally, an application to extrapolation of a seismic impulse is shown to prove our theoretical conclusions.

A least-square design approach for 2D FIR filters with arbitrary frequency response

In this paper, a least-square approach for the design of two-dimensional (2D) complex finite-impulse response (FIR) filters with arbitrary frequency response is presented. By minimizing the frequency-domain error function and revealing some of the properties of the matrices associated with the design problem, a closed-form solution is obtained. The solution is presented as an expression for the impulse response corresponding to the desired frequency-response specification. Thus, the method avoids the usual time-consuming procedures of optimization or matrix inversion, and makes a very fast calculation of the filter's coefficients possible, it is also shown that when this solution is used to design linear-phase filters and a class of 2D phase equalizers, some further computational savings can be achieved. The novel feature of the proposed approximation approach is that it can be used to design any kind of 2D FIR filters without employing any symmetry constraint on their frequency responses. Several design examples illustrating the efficiency of the approach are considered.