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The present article deals with variable viscosity on the peristaltic transport of bile in an inclined duct under the action of slip boundary conditions. The wall geometry is described by the sinusoidal wave propagating in the axial direction with different amplitude and with constant speed. The flow of fluid is examined in a wave frame of reference, moving with the velocity of the wave. Mathematical modeling of the problem includes equations of motion and continuity. The fluid flow is investigated by converting the equations into a non-dimensionalized form simplified considering long wavelength and low Reynolds number approximation. The analytic expressions for axial velocity, pressure gradient, and pressure rise over a single wavelength cycle are obtained. The impact of various parameters such as slip parameter, viscosity parameter, angle of inclination, gravity parameter and amplitude ratio on axial velocity, pressure gradient and pressure rise are discussed in detail by plotting graphs in MATLAB R2018b software. In this article, a comparison of linear and nonlinear variation of viscosity of bile has been made. It is concluded that velocity and pressure rise is more in case linear variation of viscosity, whereas more pressure gradient is required in case of nonlinear variation of viscosity.

In this paper, new designs of infinite impulse response digital integrators are presented. Transfer functions of the digital integrators are derived after utilizing the concept of multirate techniq...

This paper presents a stable, accurate and wideband microwave fractional order differentiator (MFOD) based on infinite impulse response filter. The fractional order differentiator (FOD) design prob...

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 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, 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.

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.

The implementation of stable, accurate, and wideband second-order microwave integrators (SOMIs) is presented in this paper. These designs of SOMIs are obtained by using different combinations of transmission line sections and shunt stubs in cascading. Particle swarm optimization (PSO), cuckoo search algorithm (CSA), and gravitational search algorithm (GSA) are applied to obtain the optimal values of the characteristic impedances of these line elements to approximate the magnitude response of ideal second-order integrator (SOI). The performance measure criteria for the proposed SOMIs are carried out based on magnitude response, absolute magnitude error, phase response, convergence rate, pole-zero plot, and improvement graph. The simulation results and statistical analysis demonstrate that GSA surpasses the PSO and CSA to approximate the ideal SOI in all state-of-the-art, that is eligible for wide-band microwave integrator. The designed SOMI is compact in size and suitable to cover microwave applications. The magnitude errors for the proposed SOMIs GSA based are as low as 4.9954 and 3.6573, respectively. The structure of the designed SOMI is implemented in the form of microstrip line on RT/Duroid substrate with dielectric constant 2.2 and having height 0.762 mm. The simulated and measured magnitude result agrees well with the ideal one in the frequency range of 3–15 GHz.

In this paper, an optimal design of linear phase digital finite impulse response (FIR) band stop (BS) filter using the L 1 -norm based real-coded genetic algorithm ( L 1 -RCGA) is presented. Although RCGA has proved its ability to overcome the drawbacks associated with conventional gradient-based optimization methods of filter design, it is applied here with a novel fitness function based on the L 1 -norm. This leads to a global optimal solution along with the improvement in filter design with same specifications. The designed filter pursues a better response in terms of flat passband, high stopband attenuation and fast convergence. The simulation results justify that the proposed FIR BS filter using L 1 -RCGA outperforms the existing optimization techniques, the L 1 -method and particle swarm optimization (PSO) and the conventional methods such as least-squares (LS) approach, Kaiser window method and the Parks McClellan (PM) algorithm. A detailed analysis is performed to evaluate the performance of the designed filters.

In this paper, a novel approach to design the digital linear-phase finite impulse response (FIR) differentiator is introduced. First, the differentiator design problem is formulated using the $$L_1$$ -method. Then, the $$L_1$$ optimality criterion is applied using the Bat algorithm (BA) and Particle swarm optimization (PSO) to further optimize the differentiator design. A novel fitness function is developed based on the $$L_1$$ -error norm which is unique and is liable to produce a flat response. These techniques are developed in order to minimize the non-differentiable fitness function. Finally, the simulation results have been presented for 5th-, 7th- and 11th-order FIR differentiator using the $$L_1$$ -method, PSO- $$L_1$$ and BA- $$L_1$$ . The magnitude response of the designed differentiators is analyzed for different frequency bands on the basis of relative magnitude error computed with respect to the ideal response. All the reported techniques contribute toward superior results, when compared with the traditional gradient-based optimizations, such as the window method, minimax and least-squares approach. In addition, the $$L_1$$ -method yields better results for higher-order designs. Furthermore, the proposed designs are tested on two input signals for their efficient response.

The aim of this work is to design a fractional delay second order Volterra filter that takes a discrete time sequence as input and its output is as close as possible to the output of a given nonlinear unknown system which may have higher degree nonlinearities in the least square sense. The basic reason for such a design is that rather than including higher than second degree nonlinearities in the designed system, we use the fractional delay degrees of freedom to approximate the given system. The advantage is in terms of obtaining a better approximation of the given nonlinear system than is possible by using only integer delays U+0028 since we are giving more degrees of freedom via the fractional delays U+0029 and simultaneously it does not require to incorporate higher degree nonlinearities than two. This work hinges around the fact that if the input signal is a decimated version of another signal by a factor of M, then fractional delays can be regarded as delays by integers less than M. Using the well known formula for calculating the discrete time Fourier transform U+0028 DTFT U+0029 of a decimated signal, we then arrive at an expression for the DTFT of the output of a fractional delay system in terms of the unknown first and second order Volterra system coefficients and the fractional delays. The final energy function to be minimized is the norm square of the difference between the DTFT of the given output and the DTFT of the output of the fractional delay system. Minimization over the filter coefficients is a linear problem and thus the final problem is to minimize a highly nonlinear function of the fractional delays which is accomplished using search techniques like the gradient-search and nature inspired optimization algorithms. The effectiveness of the proposed method is demonstrated using two nonlinear benchmark systems tested with five different input signals. The accuracy of the stated models using the globally convergent metaheuristic, cuckoo-search algorithm U+0028 CSA U+0029 are observed to be superior when compared with other techniques such as real-coded genetic algorithm U+0028 RGA U+0029, particle swarm optimization U+0028 PSO U+0029 and gradient-search U+0028 GS U+0029 methods. Finally, statistical analysis affirms the potential of the proposed designs for its successful implementation.

In this paper, a new meta-heuristic optimization technique, called interior search algorithm (ISA) with Lèvy flight is proposed and applied to determine the optimal parameters of an unknown infinite impulse response (IIR) system for the system identification problem. ISA is based on aesthetics, which is commonly used in interior design and decoration processes. In ISA, composition phase and mirror phase are applied for addressing the nonlinear and multimodal system identification problems. System identification using modified-ISA (M-ISA) based method involves faster convergence, single parameter tuning and does not require derivative information because it uses a stochastic random search using the concepts of Lèvy flight. A proper tuning of control parameter has been performed in order to achieve a balance between intensification and diversification phases. In order to evaluate the performance of the proposed method, mean square error (MSE), computation time and percentage improvement are considered as the performance measure. To validate the performance of M-ISA based method, simulations has been carried out for three benchmarked IIR systems using same order and reduced order system. Genetic algorithm (GA), particle swarm optimization (PSO), cat swarm optimization (CSO), cuckoo search algorithm (CSA), differential evolution using wavelet mutation (DEWM), firefly algorithm (FFA), craziness based particle swarm optimization (CRPSO), harmony search (HS) algorithm, opposition based harmony search (OHS) algorithm, hybrid particle swarm optimization-gravitational search algorithm (HPSO-GSA) and ISA are also used to model the same examples and simulation results are compared. Obtained results confirm the efficiency of the proposed method.