Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 625

# Search results for: transform order

##### 625 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function

Abstract:

Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve better decorrelation of the windowed and overlapped time signal. We present an expression that is useful for finding the perturbation in the Fractional Fourier span due to the erroneous transform order and the possible variation in the window shape and length. The expression is based on the dependency of the time-Fractional Fourier span Uncertainty on the amplitude and phase function of the signal. We also show with the help of the developed expression that the perturbation of span has a varying degree of sensitivity for varying degree of transform order and the window coefficients.
##### 624 Quality Factor Variation with Transform Order in Fractional Fourier Domain

Abstract:

Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that with the increase in the number of transients in the signal, the deviation of average Fractional Fourier span from the frequency bandwidth increases. Also, with the increase in the transient nature of the signal, the optimum value of transform order can be estimated based on the quality factor variation, and this value is found to be very close to that for which one can obtain the most compact representation. With the entire mathematical analysis and experimentation, we consolidate the fact that Fractional Fourier Transform gives more optimal representations for a number of transform orders than Fourier transform.
##### 623 Comparison of S-transform and Wavelet Transform in Power Quality Analysis

Abstract:

In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying amplitudes. The techniques include the Discrete Wavelet Transform (DWT), and the S-Transform. Several power quality problems are analyzed using both the discrete wavelet transform and S–transform, showing clearly the advantage of the S– transform in detecting, localizing, and classifying the power quality problems.
##### 622 Comparison between Higher-Order SVD and Third-order Orthogonal Tensor Product Expansion

Authors: Chiharu Okuma, Jun Murakami, Naoki Yamamoto

Abstract:

In digital signal processing it is important to approximate multi-dimensional data by the method called rank reduction, in which we reduce the rank of multi-dimensional data from higher to lower. For 2-dimennsional data, singular value decomposition (SVD) is one of the most known rank reduction techniques. Additional, outer product expansion expanded from SVD was proposed and implemented for multi-dimensional data, which has been widely applied to image processing and pattern recognition. However, the multi-dimensional outer product expansion has behavior of great computation complex and has not orthogonally between the expansion terms. Therefore we have proposed an alterative method, Third-order Orthogonal Tensor Product Expansion short for 3-OTPE. 3-OTPE uses the power method instead of nonlinear optimization method for decreasing at computing time. At the same time the group of B. D. Lathauwer proposed Higher-Order SVD (HOSVD) that is also developed with SVD extensions for multi-dimensional data. 3-OTPE and HOSVD are similarly on the rank reduction of multi-dimensional data. Using these two methods we can obtain computation results respectively, some ones are the same while some ones are slight different. In this paper, we compare 3-OTPE to HOSVD in accuracy of calculation and computing time of resolution, and clarify the difference between these two methods.
##### 621 A Novel VLSI Architecture of Hybrid Image Compression Model based on Reversible Blockade Transform

Authors: C. Hemasundara Rao, M. Madhavi Latha

Abstract:

Image compression can improve the performance of the digital systems by reducing time and cost in image storage and transmission without significant reduction of the image quality. Furthermore, the discrete cosine transform has emerged as the new state-of-the art standard for image compression. In this paper, a hybrid image compression technique based on reversible blockade transform coding is proposed. The technique, implemented over regions of interest (ROIs), is based on selection of the coefficients that belong to different transforms, depending on the coefficients is proposed. This method allows: (1) codification of multiple kernals at various degrees of interest, (2) arbitrary shaped spectrum,and (3) flexible adjustment of the compression quality of the image and the background. No standard modification for JPEG2000 decoder was required. The method was applied over different types of images. Results show a better performance for the selected regions, when image coding methods were employed for the whole set of images. We believe that this method is an excellent tool for future image compression research, mainly on images where image coding can be of interest, such as the medical imaging modalities and several multimedia applications. Finally VLSI implementation of proposed method is shown. It is also shown that the kernal of Hartley and Cosine transform gives the better performance than any other model.
##### 620 Statistical Distributions of the Lapped Transform Coefficients for Images

Authors: Vijay Kumar Nath, Deepika Hazarika, Anil Mahanta,

Abstract:

Discrete Cosine Transform (DCT) based transform coding is very popular in image, video and speech compression due to its good energy compaction and decorrelating properties. However, at low bit rates, the reconstructed images generally suffer from visually annoying blocking artifacts as a result of coarse quantization. Lapped transform was proposed as an alternative to the DCT with reduced blocking artifacts and increased coding gain. Lapped transforms are popular for their good performance, robustness against oversmoothing and availability of fast implementation algorithms. However, there is no proper study reported in the literature regarding the statistical distributions of block Lapped Orthogonal Transform (LOT) and Lapped Biorthogonal Transform (LBT) coefficients. This study performs two goodness-of-fit tests, the Kolmogorov-Smirnov (KS) test and the 2- test, to determine the distribution that best fits the LOT and LBT coefficients. The experimental results show that the distribution of a majority of the significant AC coefficients can be modeled by the Generalized Gaussian distribution. The knowledge of the statistical distribution of transform coefficients greatly helps in the design of optimal quantizers that may lead to minimum distortion and hence achieve optimal coding efficiency.

##### 619 An MADM Framework toward Hierarchical Production Planning in Hybrid MTS/MTO Environments

Authors: H. Rafiei, M. Rabbani

Abstract:

This paper proposes a new decision making structure to determine the appropriate product delivery strategy for different products in a manufacturing system among make-to-stock, make-toorder, and hybrid strategy. Given product delivery strategies for all products in the manufacturing system, the position of the Order Penetrating Point (OPP) can be located regarding the delivery strategies among which location of OPP in hybrid strategy is a cumbersome task. In this regard, we employ analytic network process, because there are varieties of interrelated driving factors involved in choosing the right location. Moreover, the proposed structure is augmented with fuzzy sets theory in order to cope with the uncertainty of judgments. Finally, applicability of the proposed structure is proven in practice through a real industrial case company. The numerical results demonstrate the efficiency of the proposed decision making structure in order partitioning and OPP location.
##### 618 Fast Cosine Transform to Increase Speed-up and Efficiency of Karhunen-Loève Transform for Lossy Image Compression

Authors: Mario Mastriani, Juliana Gambini

Abstract:

In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loève transform is applied to mentioned blocks. On the other hand, we present three new metrics based on eigenvalues for a better comparative evaluation of the techniques. Simulations show that the combined version is the best, with minor Mean Absolute Error (MAE) and Mean Squared Error (MSE), higher Peak Signal to Noise Ratio (PSNR) and better image quality. Finally, new technique was far superior to JPEG and JPEG2000.
##### 617 Projective Synchronization of a Class of Fractional-Order Chaotic Systems

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.
##### 616 Feature Level Fusion of Multimodal Images Using Haar Lifting Wavelet Transform

Abstract:

This paper presents feature level image fusion using Haar lifting wavelet transform. Feature fused is edge and boundary information, which is obtained using wavelet transform modulus maxima criteria. Simulation results show the superiority of the result as entropy, gradient, standard deviation are increased for fused image as compared to input images. The proposed methods have the advantages of simplicity of implementation, fast algorithm, perfect reconstruction, and reduced computational complexity. (Computational cost of Haar wavelet is very small as compared to other lifting wavelets.)

##### 615 A Comparative Study between Discrete Wavelet Transform and Maximal Overlap Discrete Wavelet Transform for Testing Stationarity

Abstract:

In this paper the core objective is to apply discrete wavelet transform and maximal overlap discrete wavelet transform functions namely Haar, Daubechies2, Symmlet4, Coiflet2 and discrete approximation of the Meyer wavelets in non stationary financial time series data from Dow Jones index (DJIA30) of US stock market. The data consists of 2048 daily data of closing index from December 17, 2004 to October 23, 2012. Unit root test affirms that the data is non stationary in the level. A comparison between the results to transform non stationary data to stationary data using aforesaid transforms is given which clearly shows that the decomposition stock market index by discrete wavelet transform is better than maximal overlap discrete wavelet transform for original data.

##### 614 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach

Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

##### 613 Fractional Order Feedback Control of a Ball and Beam System

Authors: Santosh Kr. Choudhary

Abstract:

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

##### 612 A Technique for Improving the Performance of Median Smoothers at the Corners Characterized by Low Order Polynomials

Authors: E. Srinivasan, D. Ebenezer

Abstract:

Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.

##### 611 A Secure Semi-Fragile Watermarking Scheme for Authentication and Recovery of Images Based On Wavelet Transform

Abstract:

Authentication of multimedia contents has gained much attention in recent times. In this paper, we propose a secure semi-fragile watermarking, with a choice of two watermarks to be embedded. This technique operates in integer wavelet domain and makes use of semi fragile watermarks for achieving better robustness. A self-recovering algorithm is employed, that hides the image digest into some Wavelet subbands to detect possible malevolent object manipulation undergone by the image (object replacing and/or deletion). The Semi-fragility makes the scheme tolerant for JPEG lossy compression as low as quality of 70%, and locate the tempered area accurately. In addition, the system ensures more security because the embedded watermarks are protected with private keys. The computational complexity is reduced using parameterized integer wavelet transform. Experimental results show that the proposed scheme guarantees the safety of watermark, image recovery and location of the tempered area accurately.

##### 610 Lower Order Harmonics Minimisation in CHB Inverter Using GA and Decomposition by WT

Abstract:

Nowadays Multilevel inverters are widely using in various applications. Modulation strategy at fundamental switching frequency like, SHEPWM is prominent technique to eliminate lower order of harmonics with less switching losses and better harmonic profile. The equations which are formed by SHE are highly nonlinear transcendental in nature, there may exist single, multiple or even no solutions for a particular MI. However, some loads such as electrical drives, it is required to operate in whole range of MI. In order to solve SHE equations for whole range of MI, intelligent techniques are well suited to solve equations so as to produce lest %THDV. Hence, this paper uses Continuous genetic algorithm for minimising harmonics. This paper also presents wavelet based analysis of harmonics. The developed algorithm is simulated and %THD from FFT analysis and Wavelet analysis are compared. MATLAB programming environment and SIMULINK models are used whenever necessary.

##### 609 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

##### 608 Empirical Mode Decomposition with Wavelet Transform Based Analytic Signal for Power Quality Assessment

Abstract:

This paper proposes empirical mode decomposition (EMD) together with wavelet transform (WT) based analytic signal for power quality (PQ) events assessment. EMD decomposes the complex signals into several intrinsic mode functions (IMF). As the PQ events are non stationary, instantaneous parameters have been calculated from these IMFs using analytic signal obtained form WT. We obtained three parameters from IMFs and then used KNN classifier for classification of PQ disturbance. We compared the classification of proposed method for PQ events by obtaining the features using Hilbert transform (HT) method. The classification efficiency using WT based analytic method is 97.5% and using HT based analytic signal is 95.5%.
##### 607 Stability of Interval Fractional-order Systems with Order 0 < α < 1

Authors: Hong Li, Shou-ming Zhong, Hou-biao Li

Abstract:

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

##### 606 Order Partitioning in Hybrid MTS/MTO Contexts using Fuzzy ANP

Authors: H. Rafiei, M. Rabbani

Abstract:

A novel concept to balance and tradeoff between make-to-stock and make-to-order has been hybrid MTS/MTO production context. One of the most important decisions involved in the hybrid MTS/MTO environment is determining whether a product is manufactured to stock, to order, or hybrid MTS/MTO strategy. In this paper, a model based on analytic network process is developed to tackle the addressed decision. Since the regarded decision deals with the uncertainty and ambiguity of data as well as experts- and managers- linguistic judgments, the proposed model is equipped with fuzzy sets theory. An important attribute of the model is its generality due to diverse decision factors which are elicited from the literature and developed by the authors. Finally, the model is validated by applying to a real case study to reveal how the proposed model can actually be implemented.
##### 605 Investigating Performance of Numerical Distance Relay with Higher Order Antialiasing Filter

Authors: Venkatesh C., K. Shanti Swarup

Abstract:

This paper investigates the impact on operating time delay and relay maloperation when 1st,2nd and 3rd order analog antialiasing filters are used in numerical distance protection. RC filter with cut-off frequency 90 Hz is used. Simulations are carried out for different SIR (Source to line Impedance Ratio), load, fault type and fault conditions using SIMULINK, where the voltage and current signals are fed online to the developed numerical distance relay model. Matlab is used for plotting the impedance trajectory. Investigation results shows that, about 75 % of the simulated cases, numerical distance relay operating time is not increased even-though there is a time delay when higher order filters are used. Relay maloperation (selectivity) also reduces (increases) when higher order filters are used in numerical distance protection.

##### 604 A Robust Hybrid Blind Digital Image Watermarking System Using Discrete Wavelet Transform and Contourlet Transform

Abstract:

In this paper, a hybrid blind digital watermarking system using Discrete Wavelet Transform (DWT) and Contourlet Transform (CT) has been implemented and tested. The implemented combined digital watermarking system has been tested against five common types of image attacks. The performance evaluation shows improved results in terms of imperceptibility, robustness, and high tolerance against these attacks; accordingly, the system is very effective and applicable.

##### 603 A Novel VLSI Architecture for Image Compression Model Using Low power Discrete Cosine Transform

Authors: Vijaya Prakash.A.M, K.S.Gurumurthy

Abstract:

In Image processing the Image compression can improve the performance of the digital systems by reducing the cost and time in image storage and transmission without significant reduction of the Image quality. This paper describes hardware architecture of low complexity Discrete Cosine Transform (DCT) architecture for image compression[6]. In this DCT architecture, common computations are identified and shared to remove redundant computations in DCT matrix operation. Vector processing is a method used for implementation of DCT. This reduction in computational complexity of 2D DCT reduces power consumption. The 2D DCT is performed on 8x8 matrix using two 1-Dimensional Discrete cosine transform blocks and a transposition memory [7]. Inverse discrete cosine transform (IDCT) is performed to obtain the image matrix and reconstruct the original image. The proposed image compression algorithm is comprehended using MATLAB code. The VLSI design of the architecture is implemented Using Verilog HDL. The proposed hardware architecture for image compression employing DCT was synthesized using RTL complier and it was mapped using 180nm standard cells. . The Simulation is done using Modelsim. The simulation results from MATLAB and Verilog HDL are compared. Detailed analysis for power and area was done using RTL compiler from CADENCE. Power consumption of DCT core is reduced to 1.027mW with minimum area[1].
##### 602 Wavelet Based Identification of Second Order Linear System

Authors: Sudipta Majumdar, Harish Parthasarathy

Abstract:

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.
##### 601 High Impedance Faults Detection Technique Based on Wavelet Transform

Authors: Ming-Ta Yang, Jin-Lung Guan, Jhy-Cherng Gu

Abstract:

The purpose of this paper is to solve the problem of protecting aerial lines from high impedance faults (HIFs) in distribution systems. This investigation successfully applies 3I0 zero sequence current to solve HIF problems. The feature extraction system based on discrete wavelet transform (DWT) and the feature identification technique found on statistical confidence are then applied to discriminate effectively between the HIFs and the switch operations. Based on continuous wavelet transform (CWT) pattern recognition of HIFs is proposed, also. Staged fault testing results demonstrate that the proposed wavelet based algorithm is feasible performance well.
##### 600 Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique

Authors: S. N. Deepa, G. Sugumaran

Abstract:

This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.

##### 599 Harmonic Parameters with HHT and Wavelet Transform for Automatic Sleep Stages Scoring

Abstract:

Previously, harmonic parameters (HPs) have been selected as features extracted from EEG signals for automatic sleep scoring. However, in previous studies, only one HP parameter was used, which were directly extracted from the whole epoch of EEG signal. In this study, two different transformations were applied to extract HPs from EEG signals: Hilbert-Huang transform (HHT) and wavelet transform (WT). EEG signals are decomposed by the two transformations; and features were extracted from different components. Twelve parameters (four sets of HPs) were extracted. Some of the parameters are highly diverse among different stages. Afterward, HPs from two transformations were used to building a rough sleep stages scoring model using the classifier SVM. The performance of this model is about 78% using the features obtained by our proposed extractions. Our results suggest that these features may be useful for automatic sleep stages scoring.
##### 598 Comparative Study of Fault Identification and Classification on EHV Lines Using Discrete Wavelet Transform and Fourier Transform Based ANN

Authors: K.Gayathri, N. Kumarappan

Abstract:

An appropriate method for fault identification and classification on extra high voltage transmission line using discrete wavelet transform is proposed in this paper. The sharp variations of the generated short circuit transient signals which are recorded at the sending end of the transmission line are adopted to identify the fault. The threshold values involve fault classification and these are done on the basis of the multiresolution analysis. A comparative study of the performance is also presented for Discrete Fourier Transform (DFT) based Artificial Neural Network (ANN) and Discrete Wavelet Transform (DWT). The results prove that the proposed method is an effective and efficient one in obtaining the accurate result within short duration of time by using Daubechies 4 and 9. Simulation of the power system is done using MATLAB.

##### 597 Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method

Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

##### 596 Modified Fast and Exact Algorithm for Fast Haar Transform

Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.