Search results for: Cosine%20similarity

Authors: Wen-Chi Hou, Cheng Luo, Zhewei Jiang, Feng Yan

Abstract:

In this research, we propose to use the discrete cosine transform to approximate the cumulative distributions of data cube cells- values. The cosine transform is known to have a good energy compaction property and thus can approximate data distribution functions easily with small number of coefficients. The derived estimator is accurate and easy to update. We perform experiments to compare its performance with a well-known technique - the (Haar) wavelet. The experimental results show that the cosine transform performs much better than the wavelet in estimation accuracy, speed, space efficiency, and update easiness.

Keywords: DCT, Data Cube

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

Abstract:

The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: Conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums.

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Authors: Jatinderdeep Kaur

Abstract:

In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

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Authors: Gaohuizi Guo, Ning Zhang

Abstract:

Firefly algorithm (FA) and Sine Cosine algorithm (SCA) are two very popular and advanced metaheuristic algorithms. However, these algorithms applied to multi-objective optimization problems have some shortcomings, respectively, such as premature convergence and limited exploration capability. Combining the privileges of FA and SCA while avoiding their deficiencies may improve the accuracy and efficiency of the algorithm. This paper proposes a hybridization of FA and SCA algorithms, named multi-objective firefly-sine cosine algorithm (MFA-SCA), to develop a more efficient meta-heuristic algorithm than FA and SCA.

Keywords: Firefly algorithm, hybrid algorithm, multi-objective optimization, Sine Cosine algorithm.

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Authors: Ali Cheraghian, Farshid Hajati, Soheila Gheisari, Yongsheng Gao

Abstract:

In this paper, we present a novel 2.5D face recognition method based on Gabor Discrete Cosine Transform (GDCT). In the proposed method, the Gabor filter is applied to extract feature vectors from the texture and the depth information. Then, Discrete Cosine Transform (DCT) is used for dimensionality and redundancy reduction to improve computational efficiency. The system is combined texture and depth information in the decision level, which presents higher performance compared to methods, which use texture and depth information, separately. The proposed algorithm is examined on publically available Bosphorus database including models with pose variation. The experimental results show that the proposed method has a higher performance compared to the benchmark.

Keywords: Gabor filter, discrete cosine transform, 2.5D face recognition, pose.

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Authors: Qiang Yang, Ping-An Du

Abstract:

Group decision making with multiple attribute has attracted intensive concern in the decision analysis area. This paper assumes that the contributions of all the decision makers (DMs) are not equal to the decision process based on different knowledge and experience in group setting. The aim of this paper is to develop a novel approach to determine weights of DMs in the group decision making problems. In this paper, the weights of DMs are determined in the group decision environment via angle cosine and projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, we define the weight of each decision maker (DM) by aggregating the angle cosine and projection between individual decision and ideal decision with associated direction indicator μ. By using the weights of DMs, all individual decisions are aggregated into a collective decision. Further, the preference order of alternatives is ranked in accordance with the overall row value of collective decision. Finally, an example in a chemical company is provided to illustrate the developed approach.

Keywords: Angel cosine, ideal decision, projection method, weights of decision makers.

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Authors: Neela. R. Rayavarapu, Neelam Rup Prakash

Abstract:

The paper discusses a computationally efficient method for the design of prototype filters required for the implementation of an M-band cosine modulated filter bank. The prototype filter is formulated as an optimum interpolated FIR filter. The optimum interpolation factor requiring minimum number of multipliers is used. The model filter as well as the image suppressor will be designed using the Kaiser window. The method will seek to optimize a single parameter namely cutoff frequency to minimize the distortion in the overlapping passband.

Keywords: Cosine modulated filter bank, interpolated FIR filter, optimum interpolation factor, prototype filter.

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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].

Keywords: Discrete Cosine Transform (DCT), Inverse DiscreteCosine Transform (IDCT), Joint Photographic Expert Group (JPEG), Low Power Design, Very Large Scale Integration (VLSI) .

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Authors: Liang-Ta Cheng, Ching-Yu Yang

Abstract:

Based on fast discrete cosine transform (FDCT), the authors present a high capacity and high perceived quality method for electrocardiogram (ECG) signal. By using a simple adjusting policy to the 1-dimentional (1-D) DCT coefficients, a large volume of secret message can be effectively embedded in an ECG host signal and be successfully extracted at the intended receiver. Simulations confirmed that the resulting perceived quality is good, while the hiding capability of the proposed method significantly outperforms that of existing techniques. In addition, our proposed method has a certain degree of robustness. Since the computational complexity is low, it is feasible for our method being employed in real-time applications.

Keywords: Data hiding, ECG steganography, fast discrete cosine transform, 1-D DCT bundle, real-time applications.

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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.

Keywords: Fast Cosine Transform, image compression, JPEG, JPEG2000, Karhunen-Loève Transform, zig-zag scan.

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Authors: Jyotsna Ogale, Alok Jain

Abstract:

In this paper newly reported Cosh window function is used in the design of prototype filter for M-channel Near Perfect Reconstruction (NPR) Cosine Modulated Filter Bank (CMFB). Local search optimization algorithm is used for minimization of distortion parameters by optimizing the filter coefficients of prototype filter. Design examples are presented and comparison has been made with Kaiser window based filterbank design of recently reported work. The result shows that the proposed design approach provides lower distortion parameters and improved far-end suppression than the Kaiser window based design of recent reported work.

Keywords: Window function, Cosine modulated filterbank, Local search optimization.

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Authors: Vinod Mishra, Dimple Rani

Abstract:

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

Keywords: Chebyshev polynomial, Numerical inverse Laplace transform, Odd cosine series.

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Authors: Ahmed A. A. Radwan, Bahgat A. Abdel Latef, Abdel Mgeid A. Ali, Osman A. Sadek

Abstract:

This study investigates the use of genetic algorithms in information retrieval. The method is shown to be applicable to three well-known documents collections, where more relevant documents are presented to users in the genetic modification. In this paper we present a new fitness function for approximate information retrieval which is very fast and very flexible, than cosine similarity fitness function.

Keywords: Cosine similarity, Fitness function, Genetic Algorithm, Information Retrieval, Query learning.

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Authors: M.Eskandari-Ghadi, M.Mahmoodian

Abstract:

In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.

Keywords: Cosine transform, Half space, Isotropic, Singular integral equation, Torsion

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Authors: El Mahdi Barrah, Said Safi, Abdessamad Malaoui

Abstract:

In this paper, we describe an application for face recognition. Many studies have used local descriptors to characterize a face, the performance of these local descriptors remain low by global descriptors (working on the entire image). The application of local descriptors (cutting image into blocks) must be able to store both the advantages of global and local methods in the Discrete Cosine Transform (DCT) domain. This system uses neural network techniques. The letter method provides a good compromise between the two approaches in terms of simplifying of calculation and classifying performance. Finally, we compare our results with those obtained from other local and global conventional approaches.

Keywords: Face detection, face recognition, discrete cosine transform (DCT), FPLBP, TPLBP, NN.

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Authors: Rehab F. Abdel-Kader, Rabab M. Ramadan, Rawya Y. Rizk

Abstract:

The recognition of human faces, especially those with different orientations is a challenging and important problem in image analysis and classification. This paper proposes an effective scheme for rotation invariant face recognition using Log-Polar Transform and Discrete Cosine Transform combined features. The rotation invariant feature extraction for a given face image involves applying the logpolar transform to eliminate the rotation effect and to produce a row shifted log-polar image. The discrete cosine transform is then applied to eliminate the row shift effect and to generate the low-dimensional feature vector. A PSO-based feature selection algorithm is utilized to search the feature vector space for the optimal feature subset. Evolution is driven by a fitness function defined in terms of maximizing the between-class separation (scatter index). Experimental results, based on the ORL face database using testing data sets for images with different orientations; show that the proposed system outperforms other face recognition methods. The overall recognition rate for the rotated test images being 97%, demonstrating that the extracted feature vector is an effective rotation invariant feature set with minimal set of selected features.

Keywords: Discrete Cosine Transform, Face Recognition, Feature Extraction, Log Polar Transform, Particle SwarmOptimization.

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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.

Keywords: VLSI, Discrete Cosine Transform, JPEG, Hartleytransform, Radon Transform

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Authors: Shimal Das, Dibyendu Ghoshal

Abstract:

Fractal based digital image compression is a specific technique in the field of color image. The method is best suited for irregular shape of image like snow bobs, clouds, flame of fire; tree leaves images, depending on the fact that parts of an image often resemble with other parts of the same image. This technique has drawn much attention in recent years because of very high compression ratio that can be achieved. Hybrid scheme incorporating fractal compression and speedup techniques have achieved high compression ratio compared to pure fractal compression. Fractal image compression is a lossy compression method in which selfsimilarity nature of an image is used. This technique provides high compression ratio, less encoding time and fart decoding process. In this paper, fractal compression with quad tree and DCT is proposed to compress the color image. The proposed hybrid schemes require four phases to compress the color image. First: the image is segmented and Discrete Cosine Transform is applied to each block of the segmented image. Second: the block values are scanned in a zigzag manner to prevent zero co-efficient. Third: the resulting image is partitioned as fractals by quadtree approach. Fourth: the image is compressed using Run length encoding technique.

Keywords: Fractal coding, Discrete Cosine Transform, Iterated Function System (IFS), Affine Transformation, Run length encoding.

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Authors: Praseeda Lekshmi.V, Dr.M.Sasikumar

Abstract:

Facial recognition and expression analysis is rapidly becoming an area of intense interest in computer science and humancomputer interaction design communities. The most expressive way humans display emotions is through facial expressions. In this paper skin and non-skin pixels were separated. Face regions were extracted from the detected skin regions. Facial expressions are analyzed from facial images by applying Gabor wavelet transform (GWT) and Discrete Cosine Transform (DCT) on face images. Radial Basis Function (RBF) Network is used to identify the person and to classify the facial expressions. Our method reliably works even with faces, which carry heavy expressions.

Keywords: Face Recognition, Radial Basis Function, Gabor Wavelet Transform, Discrete Cosine Transform

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Authors: M. Hassan, I. Osman, M. Yahia

Abstract:

This Paper proposes a new facial feature extraction approach, Wash-Hadamard Transform (WHT). This approach is based on correlation between local pixels of the face image. Its primary advantage is the simplicity of its computation. The paper compares the proposed approach, WHT, which was traditionally used in data compression with two other known approaches: the Principal Component Analysis (PCA) and the Discrete Cosine Transform (DCT) using the face database of Olivetti Research Laboratory (ORL). In spite of its simple computation, the proposed algorithm (WHT) gave very close results to those obtained by the PCA and DCT. This paper initiates the research into WHT and the family of frequency transforms and examines their suitability for feature extraction in face recognition applications.

Keywords: Face Recognition, Facial Feature Extraction, Principal Component Analysis, and Discrete Cosine Transform, Wash-Hadamard Transform.

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Authors: Jun Gil Ahn, Jong Kang Park, Jong Tae Kim

Abstract:

In this paper, we analyze major components of activity recognition (AR) in wearable device with 9-axis sensors and sensor fusion filters. 9-axis sensors commonly include 3-axis accelerometer, 3-axis gyroscope and 3-axis magnetometer. We chose sensor fusion filters as Kalman filter and Direction Cosine Matrix (DCM) filter. We also construct sensor fusion data from each activity sensor data and perform classification by accuracy of AR using Naïve Bayes and SVM. According to the classification results, we observed that the DCM filter and the specific combination of the sensing axes are more effective for AR in wearable devices while classifying walking, running, ascending and descending.

Keywords: Accelerometer, activity recognition, directional cosine matrix filter, gyroscope, Kalman filter, magnetometer.

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Authors: A. K. Bhandari, A. Kumar, P. K. Padhy

Abstract:

In this paper, a novel contrast enhancement technique for contrast enhancement of a low-contrast satellite image has been proposed based on the singular value decomposition (SVD) and discrete cosine transform (DCT). The singular value matrix represents the intensity information of the given image and any change on the singular values change the intensity of the input image. The proposed technique converts the image into the SVD-DCT domain and after normalizing the singular value matrix; the enhanced image is reconstructed by using inverse DCT. The visual and quantitative results suggest that the proposed SVD-DCT method clearly shows the increased efficiency and flexibility of the proposed method over the exiting methods such as Linear Contrast Stretching technique, GHE technique, DWT-SVD technique, DWT technique, Decorrelation Stretching technique, Gamma Correction method based techniques.

Keywords: Singular Value Decomposition (SVD), discretecosine transforms (DCT), image equalization and satellite imagecontrast enhancement.

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Authors: G. S. Walia, H. P. Singh, Padma D.

Abstract:

The integration of wide variety of communication services is made possible with invention of 3G technology. Code Division Multiple Access 2000 operates on various RF channel bandwidths 1.2288 or 3.6864 Mcps (1x or 3x systems). It is a 3G system which offers high bandwidth and wireless broadband services but its efficiency is lowered due to various factors like fading, interference, scattering, absorption etc. This paper investigates the effect of diversity (MRC), roll off factor in Root Raised Cosine (RRC) filter for the BPSK and QPSK modulation schemes. It is possible to transmit data with minimum Inter symbol Interference and within limited bandwidth with proper pulse shaping technique. Bit error rate (BER) performance is analyzed by applying diversity technique by varying the roll off factor for BPSK and QPSK. Roll off factor reduces the ISI and diversity reduces the Fading.

Keywords: CDMA2000, Diversity, Root Raised Cosine, Roll off factor.

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Authors: Say Wei Foo, Qi Dong

Abstract:

Digital watermarking is one of the techniques for copyright protection. In this paper, a normalization-based robust image watermarking scheme which encompasses singular value decomposition (SVD) and discrete cosine transform (DCT) techniques is proposed. For the proposed scheme, the host image is first normalized to a standard form and divided into non-overlapping image blocks. SVD is applied to each block. By concatenating the first singular values (SV) of adjacent blocks of the normalized image, a SV block is obtained. DCT is then carried out on the SV blocks to produce SVD-DCT blocks. A watermark bit is embedded in the highfrequency band of a SVD-DCT block by imposing a particular relationship between two pseudo-randomly selected DCT coefficients. An adaptive frequency mask is used to adjust local watermark embedding strength. Watermark extraction involves mainly the inverse process. The watermark extracting method is blind and efficient. Experimental results show that the quality degradation of watermarked image caused by the embedded watermark is visually transparent. Results also show that the proposed scheme is robust against various image processing operations and geometric attacks.

Keywords: Image watermarking, Image normalization, Singularvalue decomposition, Discrete cosine transform, Robustness.

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Authors: Tong Liu, Xuan Xu, Xiaodi Wang

Abstract:

Computational techniques derived from digital image processing are playing a significant role in the security and digital copyrights of multimedia and visual arts. This technology has the effect within the domain of computers. This research presents discrete M-band wavelet transform (MWT) and cosine transform (DCT) based watermarking algorithm by incorporating the principal component analysis (PCA). The proposed algorithm is expected to achieve higher perceptual transparency. Specifically, the developed watermarking scheme can successfully resist common signal processing, such as geometric distortions, and Gaussian noise. In addition, the proposed algorithm can be parameterized, thus resulting in more security. To meet these requirements, the image is transformed by a combination of MWT & DCT. In order to improve the security further, we randomize the watermark image to create three code books. During the watermark embedding, PCA is applied to the coefficients in approximation sub-band. Finally, first few component bands represent an excellent domain for inserting the watermark.

Keywords: discrete M-band wavelet transform , discrete M-band wavelet transform, randomized watermark, principal component analysis

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Authors: Jixin Liu, Zheming Lu

Abstract:

In this paper, a novel multipurpose audio watermarking algorithm is proposed based on Vector Quantization (VQ) in Discrete Cosine Transform (DCT) domain using the codeword labeling and index-bit constrained method. By using this algorithm, it can fulfill the requirements of both the copyright protection and content integrity authentication at the same time for the multimedia artworks. The robust watermark is embedded in the middle frequency coefficients of the DCT transform during the labeled codeword vector quantization procedure. The fragile watermark is embedded into the indices of the high frequency coefficients of the DCT transform by using the constrained index vector quantization method for the purpose of integrity authentication of the original audio signals. Both the robust and the fragile watermarks can be extracted without the original audio signals, and the simulation results show that our algorithm is effective with regard to the transparency, robustness and the authentication requirements

Keywords: Copyright Protection, Discrete Cosine Transform, Integrity Authentication, Multipurpose Audio Watermarking, Vector Quantization.

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Authors: S. Kampeephat, P. Krachodnok, R. Wongsan

Abstract:

The conventional rectangular horn has been used for microwave antenna a long time. Its gain can be increased by enlarging the construction of horn to flare exponentially. This paper presents a study of the shaped woodpile Electromagnetic Band Gap (EBG) to improve its gain for conventional horn without construction enlargement. The gain enhancement synthesis method for shaped woodpile EBG that has to transfer the electromagnetic fields from aperture of a horn antenna through woodpile EBG is presented by using the variety of shaped woodpile EBGs such as planar, triangular, quadratic, circular, gaussian, cosine, and squared cosine structures. The proposed technique has the advantages of low profile, low cost for fabrication and light weight. The antenna characteristics such as reflection coefficient (S₁₁), radiation patterns and gain are simulated by utilized A Computer Simulation Technology (CST) software. With the proposed concept, an antenna prototype was fabricated and experimented. The S₁₁ and radiation patterns obtained from measurements show a good impedance matching and a gain enhancement of the proposed antenna. The gain at dominant frequency of 10 GHz is 25.6 dB, application for X- and Ku-Band Radar, that higher than the gain of the basic rectangular horn antenna around 8 dB with adding only one appropriated EBG structures.

Keywords: Conventional Rectangular Horn Antenna, Electromagnetic Band Gap, Gain Enhancement, X- and Ku-Band Radar.

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Authors: R. Rama Kishore, Sunesh

Abstract:

This paper presents an optimized, robust, and secured watermarking technique. The methodology used in this work is the combination of entropy and chaotic grid map. The proposed methodology incorporates Discrete Cosine Transform (DCT) on the host image. To improve the imperceptibility of the method, the host image DCT blocks, where the watermark is to be embedded, are further optimized by considering the entropy of the blocks. Chaotic grid is used as a key to reorder the DCT blocks so that it will further increase security while selecting the watermark embedding locations and its sequence. Without a key, one cannot reveal the exact watermark from the watermarked image. The proposed method is implemented on four different images. It is concluded that the proposed method is giving better results in terms of imperceptibility measured through PSNR and found to be above 50. In order to prove the effectiveness of the method, the performance analysis is done after implementing different attacks on the watermarked images. It is found that the methodology is very strong against JPEG compression attack even with the quality parameter up to 15. The experimental results are confirming that the combination of entropy and chaotic grid map method is strong and secured to different image processing attacks.

Keywords: Digital watermarking, discrete cosine transform, chaotic grid map, entropy.

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Authors: H K Lakshminarayana, J S Bhat, H M Mahesh

Abstract:

A new estimator for evolutionary spectrum (ES) based on short time Fourier transform (STFT) and modified group delay function (MGDF) by signal decomposition (SD) is proposed. The STFT due to its built-in averaging, suppresses the cross terms and the MGDF preserves the frequency resolution of the rectangular window with the reduction in the Gibbs ripple. The present work overcomes the magnitude distortion observed in multi-component non-stationary signals with STFT and MGDF estimation of ES using SD. The SD is achieved either through discrete cosine transform based harmonic wavelet transform (DCTHWT) or perfect reconstruction filter banks (PRFB). The MGDF also improves the signal to noise ratio by removing associated noise. The performance of the present method is illustrated for cross chirp and frequency shift keying (FSK) signals, which indicates that its performance is better than STFT-MGDF (STFT-GD) alone. Further its noise immunity is better than STFT. The SD based methods, however cannot bring out the frequency transition path from band to band clearly, as there will be gap in the contour plot at the transition. The PRFB based STFT-SD shows good performance than DCTHWT decomposition method for STFT-GD.

Keywords: Evolutionary Spectrum, Modified Group Delay, Discrete Cosine Transform, Harmonic Wavelet Transform, Perfect Reconstruction Filter Banks, Short Time Fourier Transform.

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Authors: Valentina Koliskina

Abstract:

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functions of complex order.

Keywords: Eddy currents, magnetic permeability, Besselfunctions

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