Article
Computer Science, Artificial Intelligence
Chandan Nayak, Suman Kumar Saha, Rajib Kar, Durbadal Mandal
Summary: This article introduces an optimal design of finite impulse response-type Riesz fractional-order digital differentiator (FODD) of orders p = 0.3, 0.5, and 0.75. The design parameters of the proposed Riesz FODDs are estimated using three independent metaheuristic optimization algorithms. Experimental results show that the SSA-based design significantly outperforms the GSA and GBMO-based designs in terms of phase error and magnitude error.
Article
Computer Science, Theory & Methods
Shilpa Garg, Richa Yadav, Manjeet Kumar
Summary: This paper presents a two-dimensional (2-D) DCT interpolation based method for designing a 2-D fractional order digital differentiator (FODD). The FODD is modeled as a finite impulse response (FIR) filter. The impulse response of an ideal 2-D FODD is estimated using Grun-wald Letnikov partial fractional derivative of a two-variable function with DCT interpolation. The optimal values of the 2-D fractional order differentiator coefficients are determined using 2-D DCT-II and DCT-III methods. Simulation results show that the proposed method outperforms existing methods in terms of integral square magnitude error (ISME).
MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Engineering, Electrical & Electronic
K. R. Sreelekha, T. S. Bindiya
Summary: This work proposes a method for achieving variable bandwidth in 2D finite impulse response (FIR) filters with low implementation costs. The method uses the 2D Farrow structure to create variable 2D filters and then decomposes and approximates the 2D Farrow filter structure to obtain the final set of coefficients. Design examples of variable circular and elliptical filters are provided to illustrate the efficiency of the proposed methodology. Simulation results show that the proposed methodology can significantly reduce the number of multipliers without much degradation in performance parameters.
DIGITAL SIGNAL PROCESSING
(2023)
Article
Multidisciplinary Sciences
V. N. Stavrou, I. G. Tsoulos, Nikos E. Mastorakis
Summary: This paper investigates the transfer functions of one-dimensional and two-dimensional filters, focusing on finite impulse response and infinite impulse response filters. Various methods such as the Windows method, bilinear transformation method, designing 2-D filters from 1-D functions, and using optimization techniques for 2-D filter design are presented.
Article
Engineering, Electrical & Electronic
Huoping Yi, Xiaoping Lai
Summary: Maximally flat digital differentiators (MFDDs) are ideal for differentiating narrowband signals, but designing IIR MFDDs is challenging due to the non-convex flatness constraints. This study derived linear conditions equivalent to the non-convex constraints and successfully designed low-pass and band-pass IIR MFDDs with better responses and lower complexity. Incorporating stability constraints, the designed IIR MFSDDs exhibit improved performance compared to existing DDs.
IET SIGNAL PROCESSING
(2022)
Article
Engineering, Electrical & Electronic
Remi Garcia, Anastasia Volkova, Martin Kumm, Alexandre Goldsztejn, Jonas Kuehle
Summary: In this work, we optimally solve the problem of multiplierless design of second-order Infinite Impulse Response filters with minimum number of adders. Our one-step design approach achieves significant performance improvement on FPGA and ASIC, reducing the number of lookup tables, delay and power consumption.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Engineering, Electrical & Electronic
Anmol Gupta, Sanjay Kumar
Summary: This paper applies a new mathematical approach based on Riemann-Liouville fractional-differential operator to design fractional-order digital differentiators (FODDs). By comparing the performance of RL-FODD with well-established GL-FODD designs, the study validates the superiority and robustness of RL-FODD in achieving ideal frequency response of FODD through various experimental simulations.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Information Systems
Jehad Ababneh, Majid M. Khodier
Summary: This paper proposes a novel approach to design, optimize and improve the magnitude response and phase response linearity of IIR digital differentiators and digital integrators using the cuckoo search optimization algorithm. The designed IIR DDs and DIs based on this approach have better phase responses and better or at least comparable magnitude responses compared to those designed using other methods in the literature.
Article
Computer Science, Information Systems
Neven Mijat, Drazen Jurisic, George S. Moschytz
Summary: This paper presents a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) using a standard approach from classical circuit theory. It includes the realization of a system function by a mathematical approximation of the desired phase response and the synthesis of basic fractional-order one-port models. Simple realizations of two-port differentiator and integrator models are derived based on the presented one-ports. Illustrative examples, circuit diagrams, simulation results, and practical realizations are also provided.
Article
Optics
Dawei Wang, Hao Jiang, Guowei Liang, Qianxin Zhan, Zikang Su, Zhaohui Li
Summary: The paper introduces a method for designing chromatic dispersion equalization filter based on Fourier series, avoiding numerical evaluation of nontrivial functions and relying only on Fourier transform. The flexibility of this method is demonstrated through a filter design example of joint matched filtering and chromatic dispersion equalization.
Review
Chemistry, Analytical
Cristina I. Muresan, Isabela R. Birs, Eva H. Dulf, Dana Copot, Liviu Miclea
Summary: The manuscript discusses the applications of fractional calculus in sensing and filtering domains, including the creation of new sensors and exploration of analog filtering techniques using fractional-order components. It also highlights the development of fractional-order digital filters and their increased design flexibility and performance advantages in practical applications.
Article
Engineering, Electrical & Electronic
Wenjing Zhou, Mingwei Shen, Min Xu, Guodong Han, Yudong Zhang
Summary: In this paper, a new sparsity-optimised Farrow structure variable fractional delay (SFS-VFD) filter is proposed to address the aperture effect in wideband array. The method reduces the non-zero coefficients by exploiting coefficient (anti-)symmetry and optimising the number and orders of sub-filters. The proposed method achieves stable and fast convergence by solving the formulated cost function with regularisation constraints using the modified three-block alternating direction multiplier method (MTB-ADMM) with core variable correction items.
IET SIGNAL PROCESSING
(2023)
Article
Mathematics, Interdisciplinary Applications
Liwei Zhang, Zhanling Zhang, Ali Saleh Alshomrani, Yinghui Zhang, Lisha Wang
Summary: This study successfully applied the fuzzy partial fractional-order equation based on IIR digital filter to the monitoring of big noise data. By calculating the noise level and processing the vibration signal, accurate monitoring of noise data was achieved.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Xuefeng Zhang, Lewen Dai
Summary: This paper proposes an image enhancement algorithm based on a rough set and fractional order differentiator. By combining the rough set theory with a Gaussian mixture model, a new image segmentation algorithm with higher immunity is obtained. The algorithm can achieve better image segmentation and enhancement.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Electrical & Electronic
Jieyi Sun, Yongqing Wang, Yuyao Shen, Shaozhong Lu
Summary: In this study, a design algorithm for a variable fractional delay FIR filter based on piecewise osculating interpolation (POI) is proposed. The algorithm utilizes higher-order derivative information of the input sampling sequence and introduces two frequency-domain optimization algorithms to improve performance at high frequencies. Additionally, a one-by-one increase scheme is introduced for optimizing polynomial orders, and a two-level Farrow structure is developed for algorithm implementation.
DIGITAL SIGNAL PROCESSING
(2022)