Rajiv Saxena

On Convolution and Product Theorems for FRFT

The fractional Fourier transform (FRFT), which is considered as a generalization of the Fourier transform (FT), has emerged as a very efficient mathematical tool in signal processing for signals which are having time-dependent frequency component. Many properties of this transform are already known, but the generalization of convolution theorem of Fourier transform for FRFT is still not having a widely accepted closed form expression. In the recent past, different authors have tried to formulate convolution theorem for FRFT, but none have received acclamation because their definition do not generalize very appropriately the classical result for the FT. A modified convolution theorem for FRFT is proposed in this article which is compared with the existing ones and found to be a better and befitting proposition.

On the modified Bartlett-Hanning window (family)

Window functions have played a vital role in digital signal processing and found extensive applications in signal analysis and estimation. The definition of the modified Bartlett-Hanning (MBH) window is extended to the form:/spl omega/(t,/spl alpha/)=/spl alpha/-(4/spl alpha/-2)|t|+(1-/spl alpha/)cos2/spl pi/t;|t|/spl les/0.5, 0.5/spl les//spl alpha/<1.88 and its spectral behavior is investigated. It is found that with the parameter, /spl alpha/, adjusted to different values, this window family can attain a minimum mainlobe width of 1.08, a maximum sidelobe level of -36.89 dB and a maximum first sidelobe level of -53.59 dB. The extended MBH window family is also analyzed for other useful parameters. The property of steerable dip in the sidelobe structures is also demonstrated.

Identity verification using shape and geometry of human hands

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.

Tuning of FIR filter transition bandwidth using fractional Fourier transform

The transition bandwidth of window-based FIR filters is proportional to the window main-lobe width, which in turn is proportional to the length of the window function. As such, transition bandwidth of FIR filters can be directly tuned by varying window length for on-line tuning applications. However, analysis of window functions in fractional Fourier domain, a generalization of Fourier domain, also establishes the dependence of window main-lobe width on the order of fractional Fourier transform (FRFT). Thus, an alternative methodology to tune the transition bandwidth, based on FRFT, is developed in this work. The proposed methodology is useful for frequency domain filtering and introduces a comparative ease in tuning by eliminating the need to re-compute the impulse response coefficients. Also, significant computational saving has been achieved using FRFT. However, it is observed that the direct approach can introduce a lot more adjustability in the transition bandwidth than the FRFT approach. Apart from Kaiser window, considered to be optimum for FIR filter design, another window with a high side-lobe fall-off-rate (SLFOR), viz, Parzen-cos6(πt) (PC6), has also been used in the proposed on-line filter tuning. Better performance of windows with high SLFOR in on-line sharpening is illustrated with the aid of simulation results.

WINDOWS: A Tool in Signal Processing

Window functions have been successfully used in various areas of signal processing and communication. The role of windows is quite impressive and economical from the point of view of computational complexity and ease associated with its application. A brief description of the window functions along with their common properties and parameters is presented in this paper. A classification of all the available window functions is made and they are incorporated accordingly in a tabular manner along with their mathematical expressions (in continuous and discrete time domain) and diagrams.

An improved and simplified design of pseudo-transmultiplexer using Blackman window family

An improved and simplified approach for the design of nearly perfect reconstructed pseudo-transmultiplexer is proposed. Blackman window and its variants are used to design the prototype filter. The most important problem in the design of transmultiplexer is the existence of interference parameters like inter-channel interference (ICI) and inter-symbol interference (ISI). A generalized linear optimization technique is proposed to minimize these undesired interference parameters. The cutoff frequency of the prototype filter is selected as a variable parameter. The main feature of the proposed design scheme is that it significantly reduces the interference parameters of the transmultiplexer.

OFDM and its Major Concerns: A Study with Way Out

Abstract Orthogonal Frequency Division Multiplexing (OFDM) has been adopted as a major data transmission technique by many wireless communication standards. Despite its several advantageous features, there are some major issues which should be resolved for getting its full advantages. This paper reviews these concerns of OFDM system in detail and present different available solutions of these problems. This paper gives a great insight of major problems like high peak-to-average power ratio (PAPR) problem, synchronization (time and frequency) problems. This paper also highlights the methods of inter-carrier interference (ICI) reduction available in literature.

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

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.

Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.

An optimized transmultiplexer using combinational window functions

This paper proposes an efficient approach for the design of M-channel maximally decimated near-perfect reconstruction (NPR) type transmultiplexer. Cosine modulation is used to design the synthesis and analysis sections of the transmultiplexer. The prototype filter is designed by using high sidelobe falloff rate (SLFOR) combinational window functions. A bisection-type optimization algorithm has been applied to minimize the interference parameters like inter-channel interference (ICI) and inter-symbol interference (ISI). The proposed algorithm has certain advantages than earlier reported work. The algorithm is of generalized nature, independent of the window function used in the design of the prototype filter. Second, it is fast and computationally efficient as only a single parameter is used as a variable which provides almost uniform interference level in all subchannels. Design examples are included for comparison with earlier reported work. Very small values of ICI and ISI have been obtained by using variable and combinational window functions.