Abstract: MDS matrices are of great significance in the design
of block ciphers and hash functions. In the present paper, we
investigate the problem of constructing MDS matrices which are
both lightweight and low-latency. We propose a new method of
constructing lightweight MDS matrices using circulant matrices
which can be implemented efficiently in hardware. Furthermore, we
provide circulant MDS matrices with as few bit XOR operations as
possible for the classical dimensions 4 × 4, 8 × 8 over the space of
linear transformations over finite field F42
. In contrast to previous
constructions of MDS matrices, our constructions have achieved
fewer XORs.
Abstract: Tikhonov regularization and reproducing kernels are the
most popular approaches to solve ill-posed problems in computational
mathematics and applications. And the Fourier multiplier operators
are an essential tool to extend some known linear transforms
in Euclidean Fourier analysis, as: Weierstrass transform, Poisson
integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean
operators, partial Fourier integral, Riesz potential, Bessel potential,
etc. Using the theory of reproducing kernels, we construct a simple
and efficient representations for some class of Fourier multiplier
operators Tm on the Paley-Wiener space Hh. In addition, we give
an error estimate formula for the approximation and obtain some
convergence results as the parameters and the independent variables
approaches zero. Furthermore, using numerical quadrature integration
rules to compute single and multiple integrals, we give numerical
examples and we write explicitly the extremal function and the
corresponding Fourier multiplier operators.
Abstract: Frequency transformation with Pascal matrix
equations is a method for transforming an electronic filter (analogue
or digital) into another filter. The technique is based on frequency
transformation in the s-domain, bilinear z-transform with pre-warping
frequency, inverse bilinear transformation and a very useful
application of the Pascal’s triangle that simplifies computing and
enables calculation by hand when transforming from one filter to
another. This paper will introduce two methods to transform a filter
into a digital filter: frequency transformation from the s-domain into
the z-domain; and frequency transformation in the z-domain. Further,
two Pascal matrix equations are derived: an analogue to digital filter
Pascal matrix equation and a digital to digital filter Pascal matrix
equation. These are used to design a desired digital filter from a given
filter.
Abstract: Nonlinear evolution of broadband ultrasonic pulses
passed through the rock specimens is studied using the apparatus
“GEOSCAN-02M”. Ultrasonic pulses are excited by the pulses of Qswitched
Nd:YAG laser with the time duration of 10 ns and with the
energy of 260 mJ. This energy can be reduced to 20 mJ by some light
filters. The laser beam radius did not exceed 5 mm. As a result of the
absorption of the laser pulse in the special material – the optoacoustic
generator–the pulses of longitudinal ultrasonic waves are excited with
the time duration of 100 ns and with the maximum pressure
amplitude of 10 MPa. The immersion technique is used to measure
the parameters of these ultrasonic pulses passed through a specimen,
the immersion liquid is distilled water. The reference pulse passed
through the cell with water has the compression and the rarefaction
phases. The amplitude of the rarefaction phase is five times lower
than that of the compression phase. The spectral range of the
reference pulse reaches 10 MHz. The cubic-shaped specimens of the
Karelian gabbro are studied with the rib length 3 cm. The ultimate
strength of the specimens by the uniaxial compression is (300±10)
MPa. As the reference pulse passes through the area of the specimen
without cracks the compression phase decreases and the rarefaction
one increases due to diffraction and scattering of ultrasound, so the
ratio of these phases becomes 2.3:1. After preloading some horizontal
cracks appear in the specimens. Their location is found by one-sided
scanning of the specimen using the backward mode detection of the
ultrasonic pulses reflected from the structure defects. Using the
computer processing of these signals the images are obtained of the
cross-sections of the specimens with cracks. By the increase of the
reference pulse amplitude from 0.1 MPa to 5 MPa the nonlinear
transformation of the ultrasonic pulse passed through the specimen
with horizontal cracks results in the decrease by 2.5 times of the
amplitude of the rarefaction phase and in the increase of its duration
by 2.1 times. By the increase of the reference pulse amplitude from 5
MPa to 10 MPa the time splitting of the phases is observed for the
bipolar pulse passed through the specimen. The compression and
rarefaction phases propagate with different velocities. These features
of the powerful broadband ultrasonic pulses passed through the rock
specimens can be described by the hysteresis model of Preisach-
Mayergoyz and can be used for the location of cracks in the optically
opaque materials.
Abstract: Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.
Abstract: In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.
Abstract: Virtual touch screen using camera is an ordinary screen which uses a camera to imitate the touch screen by taking a picture of an indicator, e.g., finger, which is laid on the screen, converting the indicator tip position on the picture to the position on the screen, and moving the cursor on the screen to that position. In fact, the indicator is not laid on the screen directly, but it is intervened by the cover at some intervals. In spite of this gap, if the eye-indicator-camera angle is not large, the mapping from the indicator tip positions on the image to the corresponding cursor positions on the screen is not difficult and could be done with a little error. However, the larger the angle is, the bigger the error in the mapping occurs. This paper proposes cursor position estimation model for virtual touch screen using camera which could eliminate this kind of error. The proposed model (i) moves the on-screen pilot cursor to the screen position which locates on the screen at the position just behind the indicator tip when the indicator tip has been looked from the camera position, and then (ii) converts that pilot cursor position to the desirable cursor position (the position on the screen when it has been looked from the user-s eye through the indicator tip) by using the bilinear transformation. Simulation results show the correctness of the estimated cursor position by using the proposed model.
Abstract: Automatic currency note recognition invariably
depends on the currency note characteristics of a particular country
and the extraction of features directly affects the recognition ability.
Sri Lanka has not been involved in any kind of research or
implementation of this kind. The proposed system “SLCRec" comes
up with a solution focusing on minimizing false rejection of notes.
Sri Lankan currency notes undergo severe changes in image quality
in usage. Hence a special linear transformation function is adapted to
wipe out noise patterns from backgrounds without affecting the
notes- characteristic images and re-appear images of interest. The
transformation maps the original gray scale range into a smaller
range of 0 to 125. Applying Edge detection after the transformation
provided better robustness for noise and fair representation of edges
for new and old damaged notes. A three layer back propagation
neural network is presented with the number of edges detected in row
order of the notes and classification is accepted in four classes of
interest which are 100, 500, 1000 and 2000 rupee notes. The
experiments showed good classification results and proved that the
proposed methodology has the capability of separating classes
properly in varying image conditions.
Abstract: A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.
Abstract: Extended Kalman Filter (EKF) is probably the most
widely used estimation algorithm for nonlinear systems. However,
not only it has difficulties arising from linearization but also many
times it becomes numerically unstable because of computer round off
errors that occur in the process of its implementation. To overcome
linearization limitations, the unscented transformation (UT) was
developed as a method to propagate mean and covariance
information through nonlinear transformations. Kalman filter that
uses UT for calculation of the first two statistical moments is called
Unscented Kalman Filter (UKF). Square-root form of UKF (SRUKF)
developed by Rudolph van der Merwe and Eric Wan to
achieve numerical stability and guarantee positive semi-definiteness
of the Kalman filter covariances. This paper develops another
implementation of SR-UKF for sequential update measurement
equation, and also derives a new UD covariance factorization filter
for the implementation of UKF. This filter is equivalent to UKF but
is computationally more efficient.
Abstract: An automatic speech recognition system for the
formal Arabic language is needed. The Quran is the most formal
spoken book in Arabic, it is spoken all over the world. In this
research, an automatic speech recognizer for Quranic based speakerindependent
was developed and tested. The system was developed
based on the tri-phone Hidden Markov Model and Maximum
Likelihood Linear Regression (MLLR). The MLLR computes a set
of transformations which reduces the mismatch between an initial
model set and the adaptation data. It uses the regression class tree, as
well as, estimates a set of linear transformations for the mean and
variance parameters of a Gaussian mixture HMM system. The 30th
Chapter of the Quran, with five of the most famous readers of the
Quran, was used for the training and testing of the data. The chapter
includes about 2000 distinct words. The advantages of using the
Quranic verses as the database in this developed recognizer are the
uniqueness of the words and the high level of orderliness between
verses. The level of accuracy from the tested data ranged 68 to 85%.
Abstract: The design of a pattern classifier includes an attempt
to select, among a set of possible features, a minimum subset of
weakly correlated features that better discriminate the pattern classes.
This is usually a difficult task in practice, normally requiring the
application of heuristic knowledge about the specific problem
domain. The selection and quality of the features representing each
pattern have a considerable bearing on the success of subsequent
pattern classification. Feature extraction is the process of deriving
new features from the original features in order to reduce the cost of
feature measurement, increase classifier efficiency, and allow higher
classification accuracy. Many current feature extraction techniques
involve linear transformations of the original pattern vectors to new
vectors of lower dimensionality. While this is useful for data
visualization and increasing classification efficiency, it does not
necessarily reduce the number of features that must be measured
since each new feature may be a linear combination of all of the
features in the original pattern vector. In this paper a new approach is
presented to feature extraction in which feature selection, feature
extraction, and classifier training are performed simultaneously using
a genetic algorithm. In this approach each feature value is first
normalized by a linear equation, then scaled by the associated weight
prior to training, testing, and classification. A knn classifier is used to
evaluate each set of feature weights. The genetic algorithm optimizes
a vector of feature weights, which are used to scale the individual
features in the original pattern vectors in either a linear or a nonlinear
fashion. By this approach, the number of features used in classifying
can be finely reduced.
Abstract: This paper introduces a new signal denoising based on the Empirical mode decomposition (EMD) framework. The method is a fully data driven approach. Noisy signal is decomposed adaptively into oscillatory components called Intrinsic mode functions (IMFs) by means of a process called sifting. The EMD denoising involves filtering or thresholding each IMF and reconstructs the estimated signal using the processed IMFs. The EMD can be combined with a filtering approach or with nonlinear transformation. In this work the Savitzky-Golay filter and shoftthresholding are investigated. For thresholding, IMF samples are shrinked or scaled below a threshold value. The standard deviation of the noise is estimated for every IMF. The threshold is derived for the Gaussian white noise. The method is tested on simulated and real data and compared with averaging, median and wavelet approaches.
Abstract: Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.
Abstract: Convergence of power series solutions for a class of
non-linear Abel type equations, including an equation that arises
in nonlinear cooling of semi-infinite rods, is very slow inside their
small radius of convergence. Beyond that the corresponding power
series are wildly divergent. Implementation of nonlinear sequence
transformation allow effortless evaluation of these power series on
very large intervals..
Abstract: This paper describes a new approach of classification
using genetic programming. The proposed technique consists of
genetically coevolving a population of non-linear transformations on
the input data to be classified, and map them to a new space with a
reduced dimension, in order to get a maximum inter-classes
discrimination. The classification of new samples is then performed
on the transformed data, and so become much easier. Contrary to the
existing GP-classification techniques, the proposed one use a
dynamic repartition of the transformed data in separated intervals, the
efficacy of a given intervals repartition is handled by the fitness
criterion, with a maximum classes discrimination. Experiments were
first performed using the Fisher-s Iris dataset, and then, the KDD-99
Cup dataset was used to study the intrusion detection and
classification problem. Obtained results demonstrate that the
proposed genetic approach outperform the existing GP-classification
methods [1],[2] and [3], and give a very accepted results compared to
other existing techniques proposed in [4],[5],[6],[7] and [8].
Abstract: Recent research result has shown that two multidelay
feedback systems can synchronize each other under different
schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating
synchronization. There, the driving signal is significantly
complex due that it is constituted by multiple nonlinear transformations
of delayed state variable. In this paper, a secure communication
model is proposed based on synchronization of coupled multidelay
feedback systems, in which the plain signal is mixed with a complex
signal at the transmitter side and it is precisely retrieved at the receiver
side. The effectiveness of the proposed model is demonstrated and
verified in the specific example, where the message signal is masked
directly by the complex signal and security is examined under the
breaking method of power spectrum analysis.