arXiv subjects

Pushpendra Singh

Publications and source records attributed to Pushpendra Singh.

31 records · Page 2Linked to original sources

arXiv2018

Studies on Generalized Fourier Representations and Phase Transforms

Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier representation (GFR) that is completely based on the FR of a signal, and introduce the phase transform (PT) which is a special case of the GFR and a true generalization of the Hilbert transform. We derive the PT kernel to obtain any constant phase shift, discuss the various properties of the PT, and demonstrate that (i) a constant phase shift in a signal corresponds to variable time-delays in all harmonics, (ii) to obtain a constant time-delay in a signal, one need to provide variable phase shift in all harmonics, (iii) a constant phase shift is same as the constant time-delay only for single frequency sinusoid. The time derivative and time integral, including fractional order, of a signal can be obtained using the GFR. We propose to use discrete cosine transform (DCT) based implementation to avoid end artifacts due to discontinuities present in both end of the signal. We introduce fractional delay of a discrete time signal using the FR, and present the fast Fourier transform (FFT) implementation of all the above proposed representations. Using the analytic wavelet transform (AWT), we propose wavelet phase transform (WPT) to obtain a desired phase-shift in a signal under-analysis, and propose the two representations of wavelet quadrature transform (WQT) which is special case of the WPT where phase-shift is $π/2$ radians.

eess.SP↗

arXiv2017

A study of existing Ontologies in the IoT-domain

Several domains have adopted the increasing use of IoT-based devices to collect sensor data for generating abstractions and perceptions of the real world. This sensor data is multi-modal and heterogeneous in nature. This heterogeneity induces interoperability issues while developing cross-domain applications, thereby restricting the possibility of reusing sensor data to develop new applications. As a solution to this, semantic approaches have been proposed in the literature to tackle problems related to interoperability of sensor data. Several ontologies have been proposed to handle different aspects of IoT-based sensor data collection, ranging from discovering the IoT sensors for data collection to applying reasoning on the collected sensor data for drawing inferences. In this paper, we survey these existing semantic ontologies to provide an overview of the recent developments in this field. We highlight the fundamental ontological concepts (e.g., sensor-capabilities and context-awareness) required for an IoT-based application, and survey the existing ontologies which include these concepts. Based on our study, we also identify the shortcomings of currently available ontologies, which serves as a stepping stone to state the need for a common unified ontology for the IoT domain.

cs.AI↗

arXiv2016

Breaking the Limits -- Redefining the Instantaneous Frequency

The Carson and Fry (1937) introduced the concept of variable frequency as a generalization of the constant frequency. The instantaneous frequency (IF) is the time derivative of the instantaneous phase and it is well-defined only when this derivative is positive. If this derivative is negative, the IF creates problem because it does not provide any physical significance. This study proposes a mathematical solution and eliminate this problem by redefining the IF such that it is valid for all monocomponent and multicomponent signals which can be nonlinear and nonstationary in nature. This is achieved by using the property of the multivalued inverse tangent function. The efforts and understanding of all the methods based on the IF would improve significantly by using this proposed definition of the IF. We also demonstrate that the decomposition of a signal, using zero-phase filtering based on the well established Fourier and filter theory, into a set of desired frequency bands with proposed IF produces accurate time-frequency-energy (TFE) distribution that reveals true nature of signal. Simulation results demonstrate the efficacy of the proposed IF that makes zero-phase filter based decomposition most powerful, for the TFE analysis of a signal, as compared to other existing methods in the literature.

cs.IT↗

arXiv2016

Time-Frequency analysis via the Fourier Representation

The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the inverse Fourier transform. This study presents time-frequency analysis by the Fourier transform which maps the time-domain signal into the frequency-domain. In this study, we derive the time information from the phase of the frequency-domain signal and obtain the time-frequency representation. In order to obtain the time information in Fourier domain, we define the concept of `frequentaneous time' which is frequency derivative of phase. This is very similar to the group delay, which is also defined as frequency derivative of phase and it provide physical meaning only when it is positive. The frequentaneous time is always positive or negative depending upon whether signal is defined for only positive or negative times, respectively. If a signal is defined for both positive and negative times, then we divide the signal into two parts, signal for positive times and signal for negative times. The proposed frequentaneous time and Fourier transform based time-frequency distribution contains only those frequencies which are present in the Fourier spectrum. Simulations and numerical results, on many simulated as well as read data, demonstrate the efficacy of the proposed method for the time-frequency analysis of a signal.

cs.IT↗

arXiv2015

LINOEP vectors, spiral of Theodorus, and nonlinear time-invariant system models of mode decomposition

In this paper, we propose a general method to obtain a set of Linearly Independent Non-Orthogonal yet Energy (square of the norm) Preserving (LINOEP) vectors using iterative filtering operation and we refer it as Filter Mode Decomposition (FDM). We show that the general energy preserving theorem (EPT), which is valid for both linearly independent (orthogonal and nonorthogonal) and linearly dependent set of vectors, proposed by Singh P. et al. is a generalization of the discrete spiral of Theodorus (or square root spiral or Einstein spiral or Pythagorean spiral). From the EPT, we obtain the (2D) discrete spiral of Theodorus and show that the multidimensional discrete spirals (e.g. a 3D spiral) can be easily generated using a set of multidimensional energy preserving unit vectors. We also establish that the recently proposed methods (e.g. Empirical Mode Decomposition (EMD), Synchrosqueezed Wavelet Transforms (SSWT), Variational Mode Decomposition (VMD), Eigenvalue Decomposition (EVD), Fourier Decomposition Method (FDM), etc.), for nonlinear and nonstationary time series analysis, are nonlinear time-invariant (NTI) system models of filtering. Simulation and numerical results demonstrate the efficacy of LINOEP vectors.

cs.IT↗

arXiv2015

The Fourier Decomposition Method for nonlinear and nonstationary time series analysis

Since many decades, there is a general perception in literature that the Fourier methods are not suitable for the analysis of nonlinear and nonstationary data. In this paper, we propose a Fourier Decomposition Method (FDM) and demonstrate its efficacy for the analysis of nonlinear (i.e. data generated by nonlinear systems) and nonstationary time series. The proposed FDM decomposes any data into a small number of `Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank based multivariate FDM (MFDM) algorithm, for the analysis of multivariate nonlinear and nonstationary time series, from the FDM. We also present an algorithm to obtain cutoff frequencies for MFDM. The MFDM algorithm is generating finite number of band limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods produce the results in a time-frequency-energy distribution that reveal the intrinsic structures of a data. Simulations have been carried out and comparison is made with the Empirical Mode Decomposition (EMD) methods in the analysis of various simulated as well as real life time series, and results show that the proposed methods are powerful tools for analyzing and obtaining the time-frequency-energy representation of any data.

stat.ME↗

arXiv2015

Some studies on multidimensional Fourier theory for Hilbert transform, analytic signal and space-time series analysis

In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in multidimensional Fourier transform (MDFT), which in turn provide multidimensional spatial and space-time series analysis. The complex exponential representation of sinusoidal function always yields two frequencies, negative frequency corresponding to positive frequency and vice versa, in the multidimensional Fourier spectrum. Thus, using the MDFT, we propose multidimensional Hilbert transform (MDHT) and associated multidimensional analytic signal (MDAS) with following properties: (a) the extra and redundant positive, negative, or both frequencies, introduced due to complex exponential representation of multidimensional Fourier spectrum, are suppressed, (b) real part of MDAS is original signal, (c) real and imaginary part of MDAS are orthogonal, and (d) the magnitude envelope of a original signal is obtained as the magnitude of its associated MDAS, which is the instantaneous amplitude of the MDAS. The proposed MDHT and associated DMAS are generalization of the 1D HT and AS, respectively. We also provide the decomposition of an image into the AM-FM image model by the Fourier method and obtain explicit expression for the analytic image computation by 2DDFT.

cs.IT↗

arXiv2015

CCNCheck: Enabling Checkpointed Distributed Applications in Content Centric Networks

We consider the problem of checkpointing a distributed application efficiently in Content Centric Networks so that it can withstand transient failures. We present CCNCheck, a system which enables a sender optimized way of checkpointing distributed applications in CCN's and provides an efficient mechanism for failure recovery in such applications. CCNCheck's checkpointing mechanism is a fork of DMTCP repository CCNCheck is capable of running any distributed application written in C/C++ language.

cs.DC↗

arXiv2015

The Hilbert spectrum and the Energy Preserving Empirical Mode Decomposition

In this paper, we propose algorithms which preserve energy in empirical mode decomposition (EMD), generating finite $n$ number of band limited Intrinsic Mode Functions (IMFs). In the first energy preserving EMD (EPEMD) algorithm, a signal is decomposed into linearly independent (LI), non orthogonal yet energy preserving (LINOEP) IMFs and residue (EPIMFs). It is shown that a vector in an inner product space can be represented as a sum of LI and non orthogonal vectors in such a way that Parseval's type property is satisfied. From the set of $n$ IMFs, through Gram-Schmidt orthogonalization method (GSOM), $n!$ set of orthogonal functions can be obtained. In the second algorithm, we show that if the orthogonalization process proceeds from lowest frequency IMF to highest frequency IMF, then the GSOM yields functions which preserve the properties of IMFs and the energy of a signal. With the Hilbert transform, these IMFs yield instantaneous frequencies and amplitudes as functions of time that reveal the imbedded structures of a signal. The instantaneous frequencies and square of amplitudes as functions of time produce a time-frequency-energy distribution, referred as the Hilbert spectrum, of a signal. Simulations have been carried out for the analysis of various time series and real life signals to show comparison among IMFs produced by EMD, EPEMD, ensemble EMD and multivariate EMD algorithms. Simulation results demonstrate the power of this proposed method.

cs.IT↗

arXiv2014

The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors

It is well known that, in any inner product space, a set of linearly independent (LI) vectors can be transformed to a set of orthogonal vectors, spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM). In this paper, we propose a transformation from a set of LI vectors to a set of LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors in an inner product space and we refer it as LINOEP method. We also show that there are various solutions to preserve the square of the norm.

math.NA↗

arXiv2014

Data Driven Energy Efficiency in Buildings

Buildings across the world contribute significantly to the overall energy consumption and are thus stakeholders in grid operations. Towards the development of a smart grid, utilities and governments across the world are encouraging smart meter deployments. High resolution (often at every 15 minutes) data from these smart meters can be used to understand and optimize energy consumptions in buildings. In addition to smart meters, buildings are also increasingly managed with Building Management Systems (BMS) which control different sub-systems such as lighting and heating, ventilation, and air conditioning (HVAC). With the advent of these smart meters, increased usage of BMS and easy availability and widespread installation of ambient sensors, there is a deluge of building energy data. This data has been leveraged for a variety of applications such as demand response, appliance fault detection and optimizing HVAC schedules. Beyond the traditional use of such data sets, they can be put to effective use towards making buildings smarter and hence driving every possible bit of energy efficiency. Effective use of this data entails several critical areas from sensing to decision making and participatory involvement of occupants. Picking from wide literature in building energy efficiency, we identify five crust areas (also referred to as 5 Is) for realizing data driven energy efficiency in buildings : i) instrument optimally; ii) interconnect sub-systems; iii) inferred decision making; iv) involve occupants and v) intelligent operations. We classify prior work as per these 5 Is and dis-cuss challenges, opportunities and applications across them. Building upon these 5 Is we discuss a well studied problem in building energy efficiency -non-intrusive load monitoring (NILM) and how research in this area spans across the 5 Is.

cs.OH↗

arXiv2009

Using Resonances to Control Chaotic Mixing within a Translating and Rotating Droplet

Enhancing and controlling chaotic advection or chaotic mixing within liquid droplets is crucial for a variety of applications including digital microfluidic devices which use microscopic ``discrete'' fluid volumes (droplets) as microreactors. In this work, we consider the Stokes flow of a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we have shown in previous work that the rotation not only leads to one or more three-dimensional chaotic mixing regions, in which mixing occurs through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of chaotic mixing within the drop. Such a control was achieved through appropriate tuning of the amplitude and frequency of the rotation in order to use resonances between the natural frequencies of the system and those of the external forcing. In this paper, we study the influence of the orientation of the rotation axis on the chaotic mixing zones as a third parameter, as well as propose an experimental set up to implement the techniques discussed.

nlin.CD↗

arXiv2008

Tailored mixing inside a translating droplet

Tailored mixing inside individual droplets could be useful to ensure that reactions within microscopic discrete fluid volumes, which are used as microreactors in ``digital microfluidic'' applications, take place in a controlled fashion. In this article we consider a translating spherical liquid drop to which we impose a time periodic rigid-body rotation. Such a rotation not only induces mixing via chaotic advection, which operates through the stretching and folding of material lines, but also offers the possibility of tuning the mixing by controlling the location and size of the mixing region. Tuned mixing is achieved by judiciously adjusting the amplitude and frequency of the rotation, which are determined by using a resonance condition and following the evolution of adiabatic invariants. As the size of the mixing region is increased, complete mixing within the drop is obtained.

nlin.CD↗