This paper presents the handling of nonlinear system identification problem based on Volterra-type nonlinear systems. An efficient arithmetic optimization algorithm (AOA) along with the Kalman filter (KF) is being used for the estimation/identification purpose. The KF is proved to be a good state estimator in estimation theory. It is used to estimate the unknown variables with some given measurements observed over time. However, the performance of KF technique degrades while dealing with real-time state estimation problems. To overcome the problem encountered in KF technique, two steps are followed for nonlinear system identification. The first one involves evaluation of the KF parameters using the AOA algorithm by taking a considerable fitness function. The second step is to estimate the parameters of Volterra model using the KF method utilizing the optimal KF parameters attained in first step. In order to prove the efficiency of the proposed KF assisted AOA algorithm is further tested on various benchmark unknown Volterra models. Simulated results are reported in terms of mean square error (MSE), mean square deviation (MSD), Volterra coefficients estimation error, and fitness percentage. The results are compared with other similar algorithms such as sine cosine algorithm (SCA) assisted KF (SCA-KF), cuckoo search algorithm (CSA) assisted KF (CSA-KF), particle swarm optimization (PSO) assisted KF (PSO-KF) and genetic algorithm (GA) assisted KF (GA-KF). The reported results reveal that AOA-KF algorithm is the right choice for nonlinear system identification problem compared to the SCA-KF, CSA-KF, PSO-KF and GA-KF.

Space-time coding has the potential to achieve significant diversity gain without having channel state information at the transmitter. We apply this idea over distributed wireless relay network combined with quantized feedback. In this work, we propose and analyse the performance of imperfect feedback-based relay selection schemes employing decode and forward protocol. The feedback bit helps to select the precoder matrix at the relay node for power allocation according to the channel gain. However, a wrong relay channel may get selected due to the unguided nature of the wireless feedback link which degrades the overall performance of the considered system. Therefore, two error-tolerant weighting schemes are implemented over the considered wireless cooperative network. The exact and asymptotic expressions of the outage probability are calculated while considering imperfect feedback. The out-age performance comparison of the considered schemes over Nakagami-m faded channel with other equal power allocation and best relay selection (with and without feedback error) schemes are also investigated. It is evident from the numerical results that the considered error-tolerant schemes remain insensitive to the feedback error and provide noticeable gain.

This article demonstrates the design and implementation of a stable wideband first-order microwave integrator. The proposed design is attained by the cascading of eight equal-length serial transmission lines. The meta-heuristic optimization algorithms namely real-coded genetic algorithm, particle swarm optimization, and sine-cosine algorithm are applied to attain the characteristic impedance of serial lines. Further, the proposed integrator, fabricated on RT/Duroid 5880 substrate with permittivity (epsilon r ${\epsilon }_{r}$) = 2.2 and height ( t ) $(t)$ = 0.762 mm. The results are measured using a vector network analyzer, show its conformity with the simulated and ideal result within the frequency range of 4-18 GHz in MATLAB environment, and confirm its eligibility for Ku-band application, which is compact in size.

This paper focuses on the nonlinear system identification using butterfly optimisation algorithm (BOA) optimised with adaptive Hammerstein model which is the cascade of nonlinear second-order Volterra (SOV) and linear finite impulse response (FIR) systems. Generally, gradient-based methods have been applied for solving such problems. However, these methods may face the problem of getting trapped in local minimum solution. In this paper, a novel butterfly optimisation algorithm is used to identify the nonlinear system by using three different models, namely Hammerstein model, memoryless polynomial nonlinear (MPN)-FIR model and SOV model. Furthermore, to measure the accuracy of the employed BOA, mean square error (MSE), coefficient estimation and convergence speed are considered. To prove the efficacy of the proposed BOA, the simulated results have been compared with those of the antlion optimisation algorithm and dragonfly algorithm. The simulated results confirm that Hammerstein model with SOV-FIR optimised with BOA is able to outperform the other models and algorithms.

This paper presents a new optimal second-order design of the infinite impulse response digital differentiator. This design manifests the $$L_1$$ -error fitness function’s optimization using the multi-verse optimization algorithm. The optimizing variables are obtained from the direct wave-form-based transfer function. The acquired magnitude response approximates the ideal differentiator with the mean absolute magnitude error − 45.8842 dB. The designed optimal differentiator has also been compared with the existing designs to manifests its efficacy.

In this paper, a new transformation polynomial for s-to-z plane is presented. This third-order transformation is derived by optimising the coefficients of the logarithmic series followed by utilising the multirate technique to extend its bandwidth. In terms of magnitude and phase response, the proposed transform correlates well with the ideal and shows mean absolute magnitude error and mean absolute phase error as 40 dB and - 132.04 dB, respectively. The proposed transform is compared with the existing operators to demonstrate its performance. In addition, an example is also conferred, which establishes the viability of the transform in terms of the overall frequency response, when applied for analog-to-digital transformation.

This paper presents the FPGA implementation of half-order digital integrator configured in lattice wave digital structure. The optimal lattice wave coefficients for 3 rd and 5 th structure are obtained using the Driving Training-Based Opti-mization(DTBO) algorithm to approximate integration operator. The Simulink model of the resulting lattice wave structure shows less susceptibility compared to the traditional IIR realization for finite precision data representation. The radix $-2^{r}$ encoding based multiplication is utilized for the efficient multiplier-less implementation of the suggested lattice wave design on FPGA using Xilinx system generator for DSP.

The current study discusses Volterra series based nonlinear system models such as the Taylor series, time-delay neural network (TDNN) and nonlinear autoregressive model (NARX). The study aims to construct a truncated second-order Volterra model that can be used to identify nonlinear systems and compare their performance to that of the TDNN using benchmark cases. The feasibility of the feedback and feedforward networks is evaluated using a dataset of cortical responses evoked by wrist joint manipulation. It is observed that the TDNN is a mathematical model with more customisable parameters and requires less computation time than the Volterra system with particle swarm optimisation (PSO). Also, open-loop connections with fewer a-prior system assumptions, such as the Volterra model, can estimate 42% of wrist dynamics and closed-loop connections like the NARX model can estimate 93% of complex nonlinear dynamics.

This paper presents the fractional-order digital integrator design employing digital lattice wave structure. The ideal frequency response is approximated through the optimal lattice wave coefficients which are obtained using the ant lion optimization algorithm. In terms of the root mean square error and the quantity of multipliers, the suggested lattice wave fractional-order digital integrator performs better than the current designs.

This paper presents the handling of nonlinear system identification problem based on Volterra model. Gradient-based algorithms are generally applied to solve system identification problems. However, these algorithms have the limitation of getting trapped in the local minimum. In the presented work, a novel population-based optimization algorithm popularly known as sine cosine algorithm (SCA) is being utilized for the identification of nonlinear discrete-time system. The SCA uses mathematical sine and cosine functions for the purpose of optimization. SCA is responsible for the creation of multiple random solutions and moving them towards best solution while maintaining proper balance between the exploitation and exploration phases of optimization. The performance evaluation of the applied SCA is carried out in terms of coefficient evaluation, mean square error and convergence profile. Two different examples for nonlinear system are presented in this work so as to demonstrate the validity of the employed algorithm. Performance analysis of the proposed approach with the existing state-of-the-art algorithms proves that the SCA outperforms the other algorithms.

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, - 63.439 dB and - 78.771 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 - 56.478 dB and - 75.095 dB, respectively. The proposed designs of integrators and differentiators exhibit the precise approximation of the ideal integrator and differentiator over the full Nyquist interval.

This chapter presents the implementation of stable, accurate, and wideband second-order microwave integrators (SOMIs). These SOMI designs are obtained by the use of various cascading combinations of transmission line sections and shunt stubs. In order to obtain the optimal values of the characteristic impedances of these line elements, the particle swarm optimization (PSO), cuckoo search algorithm (CSA) and gravitational search algorithm (GSA) are used to approximate the magnitude response of the ideal second-order integrator (SOI). Based on magnitude response, absolute magnitude error, phase response, convergence rate, pole-zero plot, and improvement graph, the performance measure criteria for the proposed SOMIs are performed. The results of the simulation and statistical analysis reveal that GSA exceeds the PSO and CSA in order to approximate the ideal SOI in all state-of-the-art eligible for wide-band microwave integrator. The designed SOMI is compact and suitable for applications covering ultra-wideband (UWB). The designed SOMI structure is also simulated on Advanced Design Software (ADS) in the form of a microstrip line on a dielectric constant 2.2 RT/Duroid substrate with a height of 0.762 mm. In the 3–15 GHz frequency range, the simulated magnitude result agrees well with the ideal one.

This paper focuses on infinite impulse response (IIR) system identification which uses a recent nature inspired algorithm called antlion optimisation (ALO). The system identification problem is concerned with determining the viable parameters by minimising the cost function. Generally, gradient-based techniques are mostly used for IIR system identification. However, these traditional algorithms face the problem of getting trapped in local solution. So to get rid of this problem, a novel ALO algorithm is used for IIR system identification. The ALO is inspired by the preying process of antlions on the ants. The algorithm is free of the issues faced by the traditional techniques. The performance of ALO algorithm is measured using two measures mean square error (MSE) which is taken as cost function and the convergence profile. The results obtained using ALO are compared with those of the particle swarm optimisation (PSO) algorithm and cat swarm optimisation (CSO) algorithm. The obtained results confirmed that the algorithm surpasses the performance of the existing algorithms.

This paper presents sclera-based biometric recognition. The vessel patterns in sclera are different for every individual and this can be used to identify a person uniquely. In this analysis, we are using sobal filter and Otsu's thresholding methodology for sclera segmentation. Second we have designed a Gabor filter for sclera pattern enhancement to high light and binarize the sclera vessel patterns because the segmented sclera area is highly reflective. As a result, the sclera vascular patterns are unclear or/and have very low contrast. To accomplish the illumination impact and to achieve an illumination-invariant method, it is important to enhance the vascular patterns. Finally, we tend to plan a line-descriptor based feature extraction, registration, and matching technique. We have used the UBIRIS version one

In this paper, complimentary notch/peak filter is designed using wave digital structure and then implemented on FPGA using Xilinx System Generator for DSP EDA tool. The existing theory of all-pass filter based design is used to realize second order all-pass function using wave digital equivalent of second order resonance circuit. It is also shown that the wave digital adaptor coefficients can directly tune the frequency and bandwidth of the filter.

This paper presents a comparative analysis of the methods which to vary the pole radius of an IIR digital notch filter in order to achieve the short transient duration and high quality factor. The elimination of sinusoidal interference in the Electrocardiogram (ECG) signal has been done with the time varying pole radius notch filter. The implementation of the proposed notch filter has been done on MATLAB Simulink and Xilinx System Generator for DSP.

In this paper, two designs of first-order digital differentiators are investigated. In the first design, hybrid filter approximation is used to approximate the fractional delay-based differentiator. The second design involves the direct optimization of the first-order FIR Lagrange filter approximation. Both first-order designs are compared with the existing first-order designs in terms of absolute magnitude error to demonstrate their effectiveness.

This work is dedicated to the approximation of the integrator in the digital domain. The working principle of the proposed digital integrator (DI) optimizes the generalized transfer function based on fractional bilinear transform (FBLT) and subsequently, the multirate technique is employed to reduce the magnitude error. The obtained design correlates the corresponding ideal response and provides the absolute relative magnitude error (ARME) and the mean relative magnitude error (MRME, dB) as 0.1752 and -64.954 dB respectively. The comparison is done with the published DI ' s to show its viability in terms of low magnitude errors.

The implementation of novel, stable, accurate, and wideband infinite impulse response fractional order microwave integrators (FOMIs) is presented. The formulation of FOMIs is employed with equal length line elements in cascading. The optimum values of characteristic impedances of the line elements are determined by approximation to the ideal fractional order integrator (FOI). The hybrid algorithm (HPSO-GSA) combining particle swarm optimization (PSO) and gravitational search algorithm (GSA) which integrates PSO's exploitation and GSA's exploration ability is used. The comparison of HPSO-GSA with PSO and GSA is carried out for the proposed FOMIs. The performance criteria used are magnitude response, absolute magnitude error, phase response, pole-zero response, percentage improvement graph, and convergence rate. The simulation analysis affirms the superiority of proposed FOMI using HPSO-GSA. The absolute magnitude error of proposed 0.5 order HPSO-GSA-based FOMI is as low as 0.9436. The structure of the designed FOI is implemented with microstrip configuration on RT/Duroid substrate with permittivity 2.2 and thickness 0.762 mm that is eligible for wideband microwave integrator. The designed FOMI is compact in size and suitable to cover microwave applications. The measured results are established in fine agreement with simulation results in the frequency range of 2-9 GHz in MATLAB and Advanced Design Software environment.

In this paper, a novel method for designing an optimum infinite impulse response digital differentiator of the first and second orders is presented. The proposed method interpolates bilinear transform and rectangular transform fractionally, and then, unknown variables of the generalized equation are optimized using the genetic algorithm. The results obtained by the proposed designs are superior to all state-of-the-art designs in terms of magnitude responses. The first-order and second-order differentiator attains mean relative magnitude error as low as - 27.702 (dB) and - 35.04 (dB), respectively, in the complete Nyquist range. Besides, suggested low-order, differentiator design equations can also be optimized of any desired Nyquist frequency range, which makes it suitable for real-time applications.