Author

# Sunit K. Sen

Bio: Sunit K. Sen is an academic researcher from University of Calcutta. The author has contributed to research in topic(s): Transformation (function) & Matrix (mathematics). The author has an hindex of 5, co-authored 19 publication(s) receiving 136 citation(s).

##### Papers

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TL;DR: In this article, it is shown that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983) due to the most elemental nature of BPFs in comparison to any other PCBF function.

Abstract: It is established that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983). The superiority is mainly due to the most elemental nature of BPFs in comparison to any other PCBF function. It is also proved that the operational matrix for integration in the BPF domain is connected to the integration operational matrix in the DUSF domain by simple linear transformation involving invertible Toeplitz matrices. The transformation appears to be transparent because the integration operational matrices are found to match exactly. The reason for such transparency is explained mathematically. Finally, Hwang claimed superiority of DUSFs compared to Walsh functions in obtaining the solution of functional differential equations using a stretch matrix in the DUSF domain. It is shown that the stretch matrices of Walsh and DUSF domains are also related by linear transformation and use of any of these two matrices leads to exactly the same result. This is supported by a...

49 citations

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TL;DR: In this paper, a set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced for the analysis of control systems with SISO.

Abstract: The present work searches for a suitable set of orthogonal functions for the analysis of control systems with sample-and-hold ( S/H ). The search starts with the applicability of the well known block pulse function (BPF) set and uses an operational technique by defining a block pulse operational transfer function ( BPOTF ) to analyse a few control systems. The results obtained are found to be fairly accurate. But this method failed to distinguish between an input sampled system and an error sampled system. To remove these limitations, another improved approach was followed using a sample-and-hold operational matrix, but it also failed to come up with accurate results. Further, the method needed a large number of component block pulse functions leading to a much larger amount of storage as well as computational time. To search for a more efficient technique, a new set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced. The analysis, based upon a similar operational technique, in the SHF domain results in the same accuracy as the conventional z -transform analysis. Here, the input signal is expressed as a linear combination of sample-and-hold functions; the plant having a Laplace transfer function G(s) is represented by an equivalent sample-and-hold operational transfer function ( SHOTF ), and the output in the SHF domain is obtained by means of simple matrix multiplication. This technique is able to do away with the laborious algebraic manipulations associated with the z -transform technique without sacrificing accuracy. Also, the accuracy does not depend upon m and the presented method does not need any kind of inverse transformation. A few linear sample-and-hold SISO control systems, open loop as well as closed loop, are analysed as illustrative examples. The results are found to match exactly with the z -transform solutions. Finally, an error analysis has been carried out to estimate the upper bound of the mean integral squared error (m.i.s.e.) of the SHF approximation of a function f(t) of Lebesgue measure.

24 citations

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01 Jan 1995TL;DR: In this paper, a modification to conventional block pulse functions (BPF) is proposed by describing a set of linearly pulse-width modulated block pulse function (LPWM-BPF), which is used to develop a generalised convolution matrix of operational nature.

Abstract: A modification to conventional block pulse functions (BPF) is proposed by describing a set of linearly pulse-width modulated block pulse functions (LPWM-BPF) that has been utilised to develop a generalised convolution matrix of operational nature. This matrix is used to determine convolution of time-varying functions and is also employed to solve linear feedback system identification problem. Also, a recursive technique for solving the identification problem in the conventional BPF domain has been derived. Numerical examples are treated to establish the validity of the proposal. The representational error analysis has also been carried out for the LPWM-BPF to show that this kind of BPF set introduces less error than the conventional equal-width BPF.

20 citations

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TL;DR: In this article, a modified block Pulse Operational Transfer Function (MBPOTF) is proposed for linear SISO control system analysis in the block pulse function domain. But the results are not so accurate when compared with the direct expansion of the exact solution in the BPF domain.

Abstract: The present work makes use of the block pulse domain operational matrix for differentiation D1(m) to find out an operational transfer function. Analysis of simple control systems using this Block Pulse Operational Transfer Function (BPOTF) shows that the results are not so accurate when compared with the direct expansion of the exact solution in the BPF domain. To remove this defect, one shot operational matrices for repeated integration (OSOMRI) are obtained and these matrices are used to develop a Modified Block Pulse Operational Transfer Function (MBPOTF) for linear SISO control system analysis in the block pulse function domain. A few linear SISO control systems are analysed using the developed MBPOTF s as illustrative examples. The results are found to match exactly with the direct BPF expansions of the exact solutions.

9 citations

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01 Mar 2017

TL;DR: In this article, a new capacitor array structure which is both energy and area efficient is presented for a 4-bit successive approximation register (SAR) analog-to-digital converter (ADC).

Abstract: A new capacitor array structure which is both energy and area efficient is presented for a 4 bit successive approximation register (SAR) analog-to-digital converter (ADC). The proposed circuit consumes zero energy in the second and third comparison cycles. Significant lowering of energy in the different charge redistribution steps is ensured by applying different voltages in the switching scheme of the various comparison cycles. Besides energy saving to the extent of 98%, a 75% reduction in capacitance is achieved compared to the conventional method.

6 citations

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TL;DR: In this paper, the authors demonstrate the selective coupling of photons into the plasmon mode of a 20 nm diameter nanowire, which then propagates in a nonemissive fashion down the wire length before being emitted as an elastically scattered photon at distal end.

Abstract: We report the observation of unidirectional plasmon propagation in metallic nanowires over distances >10 μm. Through control of the incident excitation wavelength and rod composition, we demonstrate the selective coupling of photons into the plasmon mode of a 20 nm diameter nanowire. This mode then propagates in a nonemissive fashion down the wire length before being emitted as an elastically scattered photon at the distal end. As expected from previous studies of plasmon excitation in nanoparticles and thin films, we observe a strong wavelength and material dependence of this phenomenon. This metal-dependent plasmon propagation is exploited to produce a wire through which plasmons propagate unidirectionally. A bimetallic wire with a sharp Au/Ag heterojunction is shown to display both wavelength dependence and unidirectionality with respect to plasmon propagation across the heterojunction. It is expected that these results will contribute to the growing interest in optical energy transport in molecular-le...

404 citations

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TL;DR: A way to solve the fractional differential equations using the Riemann-Liouville fractional integral for repeated fractional integration and the generalized block pulse operational matrices of differentiation are proposed.

Abstract: The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.

137 citations

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TL;DR: The development and evolution of different topics related to neural networks is described showing that the field has acquired maturity and consolidation, proven by its competitiveness in solving real-world problems.

Abstract: This paper presents a comprehensive overview of modelling, simulation and implementation of neural networks, taking into account that two aims have emerged in this area: the improvement of our understanding of the behaviour of the nervous system and the need to find inspiration from it to build systems with the advantages provided by nature to perform certain relevant tasks. The development and evolution of different topics related to neural networks is described (simulators, implementations, and real-world applications) showing that the field has acquired maturity and consolidation, proven by its competitiveness in solving real-world problems. The paper also shows how, over time, artificial neural networks have contributed to fundamental concepts at the birth and development of other disciplines such as Computational Neuroscience, Neuro-engineering, Computational Intelligence and Machine Learning. A better understanding of the human brain is considered one of the challenges of this century, and to achieve it, as this paper goes on to describe, several important national and multinational projects and initiatives are marking the way to follow in neural-network research.

123 citations

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TL;DR: It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.

Abstract: The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.

85 citations

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TL;DR: In this paper, the authors used piecewise constant two-dimensional block-pulse functions (2D-BPFs) and their operational matrices for solving mixed nonlinear Volterra-Fredholm integral equations of the first kind.

Abstract: Few numerical methods such as projection methods, time collocation method, trapezoidal Nystrom method, Adomian decomposition method and some else are used for mixed Volterra–Fredholm integral equations. The main purpose of this paper is to use the piecewise constant two-dimensional block-pulse functions (2D-BPFs) and their operational matrices for solving mixed nonlinear Volterra–Fredholm integral equations of the first kind (VFIE). This method leads to a linear system of equations by expanding unknown function as 2D-BPFs with unknown coefficients. The properties of 2D-BPFs are then utilized to evaluate the unknown coefficients. The error analysis and rate of convergence are given. Finally, some numerical examples show the implementation and accuracy of this method.

47 citations