Novel class of stable wideband recursive digital integrators and differentiators

Gupta, Maneesha; Jain, Madhu; Kumar, Bipin

doi:10.1049/iet-spr.2009.0030

Cited by 48 publications

(42 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The maximum phase deviation of the proposed integratorfrom the ideal linear phase response is 33.4 o (which occurs at ω=0.57π radians). While the maximum phase deviation of the existing integrators SKG [2], Al-Alaoui optimized 4-Segment [6], Gupta-JainKumar 1 [8], and Gupta-Jain-Kumar 2 [9] from the ideal linear phase response is 35.5 o (which occurs at ω= 0.61π radians), 77.80 o (which occurs at ω= 0.80π radians), 35.3 o (which occurs at ω=0.59π radians), and 34.2 o (which occurs at ω=0.58π radians), respectively.…”

Section: Comparison Of Theproposed Integrator With the Existing Integmentioning

confidence: 99%

“…9. Results of edge detection using the proposed differentiator D N5 (z) and the existing differentiators of: Al-Alaoui optimized 3-Segment [6], Gupta-Jain-Kumar1 (GJK1) [8], Gupta-Jain-Kumar 2 (GJK2) [9], and Pei and Hsu [14] Fig. 10.…”

Section: Application Of the Proposed Digital Differentiator In Image mentioning

confidence: 99%

“…Figure 6 and Table 2 assert that the proposed differentiator D N5 (z) is the closest approximation of the ideal differentiator as compared to the existing ones.It can be seen from Figure 7 that the maximum phase deviation of the proposed differentiator from the ideal linear phase response is 10.1 o (which occurs at ω =0.74π radians). While the maximum phase deviation of the existing differentiators Al-Alaoui optimized 3-Segment [6], Gupta-JainKumar 1 [8], Gupta-Jain-Kumar 2 [9], and Pei and Hsu [14] …”

Section: Comparison Of the Proposed Differentiator With The Existing mentioning

confidence: 99%

“…The objective is to design these differintegrators so that they meet the given requirements with sufficient accuracy. Various approximations of ideal differintegrators have been reported in the literature [1][2][3][4][5][6][7][8][9]. Al-Alaoui [1] has proposed the interpolation method to design a digital integrator.…”

Section: Introductionmentioning

confidence: 99%

“…A family of digital integrators and differentiators has also been proposed by Al-Alaoui [6] by using interpolation and a simulated annealing optimization method. Gupta-Jain-Kumar (GJK) [7][8][9] have also proposed digital integrators by using the interpolation method. These approximations only meet the magnitude or linear phase requirement, but do not meet both simultaneously.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Design of the IIR Differintegrator and its Application in Edge Detection

Jain¹,

Gupta²,

Jain³

2014

Journal of Information Processing Systems

View full text Add to dashboard Cite

Abstract-New IIR digital differintegrators (differentiator and integrator) with very minor absolute relative errors are presented in this paper. The digital integrator is designed by interpolating some of the existing integrators. The optimum value of the interpolation ratio is obtained through linear programming optimization. Subsequently, by modifying the transfer function of the proposed integrator appropriately, new digital differentiator is obtained. Simulation results demonstrate that the proposed differintegrator are a more accurate approximation of ideal ones, than the existing differintegrators. Furthermore, the proposed differentiator has been tested in an image processing application. Edges characterize boundaries and are, therefore, a problem of fundamental importance in image processing. For comparison purpose Prewitt, Sobel, Roberts, Canny, Laplacian of Gaussian (LOG), Zerocross operators were used and their results are displayed. The results of edge detection by some of the existing differentiators are also provided. The simulation results have shown the superiority of the proposed approach over existing ones.

show abstract

Section: Comparison Of Theproposed Integrator With the Existing Integmentioning

confidence: 99%

Section: Application Of the Proposed Digital Differentiator In Image mentioning

confidence: 99%

Section: Comparison Of the Proposed Differentiator With The Existing mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Design of the IIR Differintegrator and its Application in Edge Detection

Jain¹,

Gupta²,

Jain³

2014

Journal of Information Processing Systems

View full text Add to dashboard Cite

show abstract

Design of recursive digital integrators and differentiators using particle swarm optimization

Jalloul

Al-Alaoui

2015

Circuit Theory & Apps

View full text Add to dashboard Cite

This paper presents a new method for designing digital recursive integrators and differentiators by using nonlinear stochastic global optimization based on particle swarm optimization (PSO). A modified PSO is used to optimize the unknown coefficients of second-order and third-order recursive integrators in order to obtain a better magnitude response closer to the ideal integrator. The coefficients of the state-of-theart available filters in the literature are chosen as initial points in the PSO process. By choosing a good starting point, convergence to an optimal solution is greatly facilitated. A dynamic modification of the fitness function used in the PSO process leads to the design of a set of digital integrators each optimized for a specific frequency range. Then, second-order and third-order recursive digital differentiators are designed by inverting and stabilizing the transfer functions of the designed recursive integrators. The obtained stabilized differentiators are further optimized using PSO to further improve their performance. The magnitude responses of the designed filters outperform the existing integrators and differentiators.Additionally Al-Alaoui in [2] proposed an approach to design a digital differentiator by inverting the transfer function of an integrator with similar specifications, stabilizing the resulting transfer function, and compensating the resulting change in magnitude because of the stabilization step that consisted of reflecting the resulting poles, the zeros of the integrator, that lie outside the unit circle at a radius r in the z-plane to 1/r. In [3], he obtained a class of second-order integrators and the corresponding differentiators by interpolating the Simpson and the trapezoidal integration rules and inverting the transfer functions of the obtained integrators.Ngo [4] employed Newton-Cotes integration method to design digital integrators. Tseng-Lee [5] used fractional delay to design digital integrators and Pei and Hsu [6] proposed employing fractional delay filters to obtain new differentiators. Gupta, Jain, and Kumar [7-9] developed digital integrators by interpolating some of the popular digital integration techniques. Varshney, Gupta, and Visweswaran [10] also used the interpolation method to design new digital differentiators. Some recent publications [11][12][13][14] in this field have also been reported in the literature.Recursive digital integrator's design can be formulated as an optimization problem where one searches for the optimal vector of filter coefficients to minimize a certain error function between the designed filter and the ideal integrator given by 1/jw. The previously mentioned methods for designing digital integrators suffer from poor accuracy because only a small fraction of the entire set of candidate vectors of filter coefficients is considered and thus are easily trapped into local optima on the error surface. Papamarkos and Chamzas [15] have used linear programming optimization method to propose the design of digital integrators. Lai, Lin, and ...

show abstract

Optimal design of wideband digital integrators and differentiators using harmony search algorithm

Mahata

Saha

Kar

et al. 2016

Int J Numerical Modelling

View full text Add to dashboard Cite

This paper presents an efficient approach to design stable, wideband, and infinite impulse response digital integrators (DIs) and digital differentiators (DDs) of first, second, third, and fourth order using an evolutionary optimization algorithm called harmony search (HS). In recent years, although wideband DIs and DDs have been designed using metaheuristic optimization techniques such as simulated annealing, genetic algorithm, and particle swarm optimization (PSO), these algorithms lead to sub‐optimal solutions because of stagnation and premature convergence. HS algorithm, however, promises an enhanced frequency response for DIs and DDs because of the better exploration and exploitation of the search space. Simulation results demonstrate the superiority of HS‐based designs as compared with three well‐known benchmark evolutionary optimization algorithms, namely real coded genetic algorithm (RGA), PSO, and differential evolution (DE) based designs by yielding the least values of different magnitude response error metrics. Parametric and non‐parametric statistical hypothesis tests are also conducted to compare the consistency in the performance of HS‐based DIs and DDs with those of the designs based on RGA, PSO, and DE. The proposed HS‐based designs also outperform those of the designs based on both classical and evolutionary optimization approaches reported in recent literature in terms of the maximum absolute magnitude error metric.

show abstract

Novel class of stable wideband recursive digital integrators and differentiators

Cited by 48 publications

References 20 publications

The Design of the IIR Differintegrator and its Application in Edge Detection

The Design of the IIR Differintegrator and its Application in Edge Detection

Design of recursive digital integrators and differentiators using particle swarm optimization

Optimal design of wideband digital integrators and differentiators using harmony search algorithm

Contact Info

Product

Resources

About