Rajiv Saxena

Bio: Rajiv Saxena is an academic researcher from Jaypee University of Engineering and Technology. The author has contributed to research in topics: Fractional Fourier transform & Window function. The author has an hindex of 17, co-authored 115 publications receiving 1086 citations. Previous affiliations of Rajiv Saxena include Madhav Institute of Technology and Science & Jaypee Institute of Information Technology.

Fractional Fourier transform: A novel tool for signal processing

Abstract: The fractional Fourier transform (FRFT) is the generalization of the classical Fourier transform. It depends on a parameter ? (= a ?/2) and can be interpreted as a rotation by an angle ? in the time-frequency plane or decomposition of the signal in terms of chirps. This paper discusses discrete FRFT (DFRFT), time-frequency distributions related to FRFT, optimal filter and beamformer in FRFT domain, filtering using window functions and other fractional transforms along with simulation results.

Identity verification using shape and geometry of human hands

Abstract: Shape and geometry features are encoded from contour of the hand only.Robust preprocessing is introduced to cope with the noise and disjoint fingers.Hand orientation and finger registration is applied to provide more flexibility.Two level score fusion is adopted to enhance the verification performance.Promising results are obtained over contact and contactless (IITD) datasets. A multimodal biometric system for personal identity verification is proposed using hand shape and hand geometry in this paper. Shape and geometry features are derived with the help of only contour of the hand image for which only one image acquisition device is sufficient. All the processing is done with respect to a stable reference point at wrist line which is more stable as compared to the centroid against the finger rotation and peaks and valleys determination. Two shape based features are extracted by using the distance and orientation of each point of hand contour with respect to the reference point followed by wavelet decomposition to reduce the dimension. Seven distances are used to encode the geometrical information of the hand. Shape and geometry based features are fused at score levels and their performances are evaluated using standard ROC curves between false acceptance rate, true acceptance rate, equal error rate and decidability index. Different similarity measures are used to examine the accuracy of the introduced method. Performance of system is analyzed for shape based (distance and orientation) and geometrical features individually as well as for all possible combinations of feature and score level fusion. The proposed features and fusion methods are studied over two hand image datasets, (1) JUET contact database of 50 subjects having 10 templates each and (2) IITD contactless dataset of 240 subjects with 5 templates each. The proposed method outperforms other approaches with the best 0.31% of EER.

Multirate Systems and Filterbanks

Abstract: Window functions have been successfully used in various areas such as filtering, beam forming and multirate signal processing. Due to available closed form expressions, the role of windows is economical. One of the key applications is the design of FIR filters. These filters are used in decimators and interpolators which are the basic building blocks for any multirate system and filterbank. In present scenario, a system with an improved performance, better quality, little error is the prime requirement. With this objective FIR multirate filters are designed using window functions. These functions can be used to design half-band filters where fifty percent filter coefficients result with zero value. With bandpass filters more than seventy percent zero valued coefficients are obtained if they preserved the concept of half-band symmetry. On the basis of error criterion filterbanks are of two types, viz., pseudo filterbanks and perfect reconstructed filterbanks. A new linear optimization algorithm is applied to obtain the pseudo filterbanks. Lag windows can be used to design energy efficient filters called compaction filters. The compaction gain is very near to optimal ones.

Fractal Antennas: A Novel Miniaturization Technique for Wireless Communications

Abstract: Wireless applications, particularly with multiple resonances, put new demands on antennas pertaining to size, gain, efficiency, bandwidth, and more. One promising approach in this regard is to use fractal geometries to find the best distribution of currents within a volume to meet a particular design goal. In the miniaturization of wire antennas it has been found that the electromagnetic coupling between wire angles limits the reduction of the resonant frequency with increasing wire length. Recent efforts by several researchers around the world to combine fractal geometry with electromagnetic theory have led to an emergence of new and innovative antenna designs. Unique properties of fractals have been exploited to develop a new class of antenna-element designs that are multi-band and compact in size and have been shown to possess several highly desirable properties, including multi-band performance, low sidelobe levels, and its ability to develop rapid beamforming algorithms based on the recursive nature of fractals. The purpose of this paper is to introduce the concept of the fractals and to provide a study and implementation of rapidly growing field of fractal antenna engineering including recent developments. The simulated results for Koch fractal antenna using AWAS and NEC are also provided.

Fractional Fourier Transform and Fractional-Order Calculus-Based Image Edge Detection

Abstract: Edge detection is an integral component of image processing to enhance the clarity of edges in an image. Detection of edges for an image may help for image segmentation, data compression, and image reconstruction. Edges of an image are considered a type of crucial information that can be extracted by applying detectors with different methodologies. Its main purpose is to simplify the image data in order to minimize the amount of data to be processed. There exist many rich classical edge detection techniques which make use of integer-order differentiation operators and can function in both spatial and frequency domains. In the case of integer-order differentiation operators, the gradient operator is identified by order `one' and the Laplacian by order `two.' This paper demonstrates a new kind of edge detector based on the `fractional' (`non-integer')-order differentiation operation and through the usage of the `fractional Fourier transformation' tool, so as to perform it in the fractional Fourier frequency domain, known as the edge detection based on fractional signal processing approach. It is shown through computer simulations that this approach can detect the edges precisely and efficiently. Finally, the performance of the proposed methodology is illustrated from the quantitative aspects of mean square error and peak signal-to-noise ratio through simulations. The experiments show that, for any grayscale image, this method can obtain better edge detection performance to satisfy human visual sense. Moreover, comparisons are also provided to prove that the proposed method outperforms the classical edge detection operators, interpreted in terms of robustness to noise.

Table Of Integrals Series And Products

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Non-Lagrangian Models of Current Algebra

Abstract: An alternative is proposed to specific Lagrangian models of current algebra. In this alternative there are no explicit canonical fields, and operator products at the same point [say, ${j}_{\ensuremath{\mu}}(x){j}_{\ensuremath{\mu}}(x)$] have no meaning. Instead, it is assumed that scale invariance is a broken symmetry of strong interactions, as proposed by Kastrup and Mack. Also, a generalization of equal-time commutators is assumed: Operator products at short distances have expansions involving local fields multiplying singular functions. It is assumed that the dominant fields are the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ currents and the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ multiplet containing the pion field. It is assumed that the pion field scales like a field of dimension $\ensuremath{\Delta}$, where $\ensuremath{\Delta}$ is unspecified within the range $1\ensuremath{\le}\ensuremath{\Delta}l4$; the value of $\ensuremath{\Delta}$ is a consequence of renormalization. These hypotheses imply several qualitative predictions: The second Weinberg sum rule does not hold for the difference of the ${K}^{*}$ and axial-${K}^{*}$ propagators, even for exact $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$; electromagnetic corrections require one subtraction proportional to the $I=1$, ${I}_{z}=0\ensuremath{\sigma}$ field; $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ and ${\ensuremath{\pi}}_{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ are allowed by current algebra. Octet dominance of nonleptonic weak processes can be understood, and a new form of superconvergence relation is deduced as a consequence. A generalization of the Bjorken limit is proposed.

Multirate digital signal processing

Abstract: There has been a great deal of material in the area of discrete-time transforms that has been published in recent years. This book does an excellent job of presenting important aspects of such material in a clear manner. The book has 11 chapters and a very useful appendix. Seven of these chapters are essentially devoted to the Fourier series/transform, discrete Fourier transform, fast Fourier transform (FFT), and applications of the FFT in the area of spectral estimation. Chapters 8 through 10 deal with many other discrete-time transforms and algorithms to compute them. Of these transforms, the KarhunenLoeve, the discrete cosine, and the Walsh-Hadamard transform are perhaps the most well-known. A lucid discussion of number theoretic transforms i5 presented in Chapter 11. This reviewer feels that the authors have done a fine job of compiling the pertinent material and presenting it in a concise and clear manner. There are a number of problems at the end of each chapter, an appreciable number of which are challenging. The authors have included a comprehensive set of references at the end of the book. In brief, this book is a valuable contribution to the general areas of signal processing and communications. It can be used for a graduate level course in perhaps two ways. One would be to cover the first seven chapters in great detail. The other would be to cover the whole book by focussing on different topics in a selective manner. This book by Elliott and Rao is extremely useful to researchers/engineers who are working in the areas of signal processing and communications. It i s also an excellent reference book, and hence a valuable addition to one’s library

Risk Factors and Preventions of Breast Cancer.

Abstract: Breast cancer is the second leading cause of cancer deaths among women. The development of breast cancer is a multi-step process involving multiple cell types, and its prevention remains challenging in the world. Early diagnosis of breast cancer is one of the best approaches to prevent this disease. In some developed countries, the 5-year relative survival rate of breast cancer patients is above 80% due to early prevention. In the recent decade, great progress has been made in the understanding of breast cancer as well as in the development of preventative methods. The pathogenesis and tumor drug-resistant mechanisms are revealed by discovering breast cancer stem cells, and many genes are found related to breast cancer. Currently, people have more drug options for the chemoprevention of breast cancer, while biological prevention has been recently developed to improve patients' quality of life. In this review, we will summarize key studies of pathogenesis, related genes, risk factors and preventative methods on breast cancer over the past years. These findings represent a small step in the long fight against breast cancer.