Infinite Impulse Response Digital Integrators Research Articles

Fractional interpolation and multirate technique based design of optimum IIR integrators and differentiators

ABSTRACT In this paper, new designs of infinite impulse response digital integrators are presented. Transfer functions of the digital integrators are derived after utilising the concept of multirate technique in the fractional interpolation of the rectangular and bilinear transform. Thereafter, the unknown variables of the obtained generalised transfer functions are optimised by using the optimisation algorithm. This yields the mean relative magnitude error, dB and dB for the first- and second-order, respectively. Furthermore, new designs of the first- and second-order digital differentiators are obtained by inverting the generalised transfer functions of the proposed integrator designs followed by optimisation of the unknown variables. The mean relative magnitude errors for first- and second-order differentiators are obtained as dB and dB, respectively. The proposed designs of integrators and differentiators exhibit the precise approximation of the ideal integrator and differentiator over the full Nyquist interval.

Optimal design of IIR wideband digital differentiators and integrators using salp swarm algorithm

This paper proposes an approach based on a weighted L1-norm optimization criterion and employs it in conjunction with salp swarm algorithm (SSA) to design 2nd- to 4th-order wideband infinite impulse response (IIR) digital differentiators (DDs). Integration of the proposed fitness function and SSA allows both the magnitude and phase responses to be improved. An extensive simulation is carried out to explore the performance of the proposed approach. First, a comparative study with widely used methods, namely, real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO), is performed to examine accuracy, robustness, consistency and efficiency. Afterwards, the magnitude and phase responses of the proposed digital differentiators are compared with those of the existing designs in the literature. New wideband IIR digital integrators (DIs) are derived by inverting transfer functions of their respective digital differentiators and then compared with the existing designs in the literature in terms of the magnitude and phase responses. Simulation and statistical results reveal that the superiority of the proposed approach is statistically significant and demonstrate that the proposed digital differentiators and integrators significantly outperform all state-of-the-art designs in terms of the magnitude response as measured by the absolute relative error (ARE) with almost linear phase responses in wideband frequency regions.

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

AbstractThis 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.

Class of digital integrators and differentiators

A novel class of infinite impulse response digital integrators and differentiators is developed. A class of digital integrators is first derived from a class of numerical integration rules. A class of digital differentiators is then obtained by inverting the transfer functions of the obtained integrators and stabilising the resulting transfer functions together with magnitude compensation if necessary. Simulated annealing is applied to optimise some of the obtained integrators and differentiators.

Closed-Form Design of Digital IIR Integrators Using Numerical Integration Rules and Fractional Sample Delays

In this paper, the numerical integration rules and fractional sample delays will be used to obtain the closed-form design of infinite-impulse response (IIR) digital integrators. There are two types of numerical integration rules to be investigated. One is Newton-Cotes quadrature rule, the other is Gauss-Legendre integration rule. Although the proposed IIR digital integrators will involve the implementation of fractional sample delays, this problem is easily solved by applying well-documented design techniques of the finite-impulse response Lagrange and IIR allpass fractional delay filters. Several design examples are illustrated to demonstrate the effectiveness of the proposed method