Sunit K. Sen

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

Walsh Functions and their Applications: A Review

Abstract: The piecewise constant Walsh function is not new in the field of mathematics because it was proposed in the year 1923 by J L Walsh. But its suitability to qualify as an elegant mathematical tool for the analysis of physical systems became apparent to the researchers quite late. Though other functions of the same piecewise constant orthogonal class attracted attentions of scientists as well as technologists to find frequent applications, the Walsh function has maintained its leadership among its clan having wide application areas ranging from the field of communication to the area of systems and control. The applications encompass die areas of digital signal processing image processing, logic circuit design etc.The present paper gives an overview of the Walsh analysis with special stress upon its application in the fields of communication, systems, control and other areas as well. The paper also reviews other non-sinusoidal orthogonal functions of the same class. Considering the present state of applicatio...

Analysis of linear discrete SISO control systems via a set of delta functions

Abstract: The paper presents a computational technique through operational matrices using a set of mutually disjoint delta functions (DF) for the analysis of linear discrete control systems. Following a brief review of the well known block pulse functions (BPF), a new set of delta functions is viewed in the same light. This set is used to develop operational transfer functions in the delta function domain (DOTF) and employed for discrete system analysis which results in the same accuracy as the conventional z-transform method. The presented technique uses simple matrix manipulations and is able to do away with laborious and involved algebraic steps, including inverse transformation, associated with the z-transform analysis without losing accuracy. Also, the accuracy of sample values of the output does not depend upon m (or the sampling interval h). A few linear discrete SISO control systems, open loop as well as closed loop, having different typical plant transfer functions, are analysed as illustrative examples.

Optical Computing Techniques

Abstract: A review of the contemporary issues in optical computing is presented. The optical systems and techniques which are used to implement different functional sub units of a digital computer are elaborated. Several architectures that are being explored for digital optical computing are described. Some issues relating to organisational and functional aspects of optical computing, such as cellular automata, symbolic substitution, optical artificial intelligence and optical neural network are also discussed.

A new set of pulse-width modulated generalized block pulse functions (PWM-GBPF) and its application to cross-/auto-correlation of time-varying functions

Abstract: The present work proposes a significant modification to conventional block pulse functions (BPF) by describing a novel set of pulse-width modulated generalized block pulse functions (PWM-GBPF) which has been utilized to develop generalized correlation matrices of operational nature. These matrices are used to determine cross-/auto-correlation of time-varying functions. Numerical examples are treated to establish the validity of the proposal. Also, a representational error analysis has been carried out for the PWM-GBPF to show that this kind of BPF set introduces a smaller error than the conventional equal width BPF

A microprocessor based new software technique for global Walsh function generation

Abstract: Walsh function and Walsh transform are important analytical and hardware tools for signal processing and have found wide applications in digital communications as well as in digital image processing. Therefore the use of Walsh function generator is very frequent in the above fields. Implementation of such a generator through hardware logic may give rise to orthogonality error in the generated function set. This paper presents a new software technique for a global Walsh function generator which removes orthogonality error. Further, the presented technique allows one to generate the Walsh function set in three different orders, namely, Natural (or Hadamard) order, Dyadic (or Paley) order and Sequency (or Walsh) order. Using an INTEL 8085 microprocessor the first 16 Walsh functions are generated as an illustration of the proposed software.

Unidirectional Plasmon Propagation in Metallic Nanowires

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...

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

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.

A new set of orthogonal functions and its application to the analysis of dynamic systems

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.