A new approach for the design of digital integrators

Papamarkos, Nikos; Chamzas, C.

doi:10.1109/81.536749

Cited by 59 publications

(47 citation statements)

References 5 publications

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“…Further, the percentage relative errors (PREs) of the obtained recursive digital differentiators from the ideal differentiators of corresponding time-constants are shown in Figure 2. From Figures 1 and 2, it is observed that the few optimized designs for non unity time-constants may be wideband with lower percentage relative error compared to the unity timeconstant design as in (11). As an example, the proposed design of proportion constant (13) can also be converted to design a recursive digital differentiator of unity time-constant.…”

Section: Design Methodologymentioning

confidence: 99%

“…The corresponding digital differentiator of unity time-constant is given in (16). The recursive wideband digital integrators can be easily obtained by inverting the transfer functions of proposed recursive digital differentiators as in (11)(12)(13)(14)(15)(16). Table 2 shows the values of proportion constants i K with the corresponding timeconstants for different designs of recursive digital integrators.…”

Section: Design Methodologymentioning

confidence: 99%

“…Later, Al-Alaoui has proposed several designs of recursive digital differentiators and integrators by using various techniques for lower percentage relative errors as in [7][8][9][10]. A linear programming optimization approach is also proposed to design recursive digital integrators and differentiators [11]. Later, Ngo has proposed wideband digital integrator and differentiator of third-order based on Newton-Cotes integration rule.…”

Section: Introductionmentioning

confidence: 99%

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A Simple Approach to Design Recursive Digital Differentiators and Integrators

Upadhyay¹,

Singh²

2011

IJCA

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In this paper, a simple approach is proposed to design recursive digital differentiators and integrators by applying the concept of time-constant analysis. The time-constant combined with the magnitude response describes the system behavior of a digital differentiator and an integrator. Further, new recursive digital differentiator and integrator designs of first-order systems are also obtained for more accurate or comparable magnitude responses as compared to the existing designs of higher-order systems over wideband. These designs are more suitable for control systems and signal processing applications.

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Section: Design Methodologymentioning

confidence: 99%

Section: Design Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Simple Approach to Design Recursive Digital Differentiators and Integrators

Upadhyay¹,

Singh²

2011

IJCA

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“…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%

“…Schneider et al [2] have also proposed a digital integrator by modifying the Newton-Cotes integration rule. Papamarkos and Chamzas [3] used the linear programming optimization method in designing digital integrators. Ngo [4] used the closed form of the Newton-Cotes integration rule to design a digital integrator.…”

Section: Introductionmentioning

confidence: 99%

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

Jain¹,

Gupta²,

Jain³

2014

Journal of Information Processing Systems

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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.

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Design of recursive digital integrators and differentiators using particle swarm optimization

Jalloul

Al-Alaoui

2015

Circuit Theory & Apps

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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 ...

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A new approach for the design of digital integrators

Cited by 59 publications

References 5 publications

A Simple Approach to Design Recursive Digital Differentiators and Integrators

A Simple Approach to Design Recursive Digital Differentiators and Integrators

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

Design of recursive digital integrators and differentiators using particle swarm optimization

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