• Journal of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1105-1127
• /
• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Journal of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.709-723
• /
• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.14 no.5
• /
• pp.458-465
• /
• 2003

In this paper, we analyze the transient electromagnetic response from three-dimensional(3-D) dielectric bodies using a time-domain electric field integral equation formulation. The solution method in this paper is based on the Galerkin＇s method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated as an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed method are presented.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.17 no.7 s.124
• /
• pp.638-648
• /
• 2007

A principal components analysis of the entire median HRIRs in the CIPIC HRTF database reveals that the individual HRIRs can be adequately reconstructed by a linear combination of several orthonormal basis functions. The basis functions represent the inter-individual and inter-elevation variations in median HRIRs. There exist elevation-dependent tendencies in the weights of basis functions, and the basis functions can be ordered according to the magnitude of standard deviation of the weights at each elevation. We propose a HRIR customization method via tuning of the weights of 3 dominant basis functions corresponding to the 3 largest standard deviations at each elevation. Subjective listening test results show that both front-back reversal and vertical perception can be improved with the customized HRIRs.

• Proceedings of the KOSOMBE Conference
• /
• v.1994 no.12
• /
• pp.31-38
• /
• 1994

This paper proposed signal decomposition and multiresolution representation through wavelet transform using wavelet orthonormal basis. And it suggested most appropriate filter for scaling function in multiresoltion representation and compared two compression method, arithmetic coding and Huffman coding. Results are as follows 1. Daub18 coefficient is most appropriate in computing time, energy compaction, image quality. 2. In case of image browsing that should be small in size and good for recognition, it is reasonable to decompose to 3 scale using pyramidal algorithm. 3. For the case of progressive transmittion where requires most grateful image reconstruction from least number of sampls or reconstruction at any target rate, I embedded the data in order of significance after scaling to 5 step. 4. Medical images such as information loss is fatal have to be compressed by lossless method. As a result from compressing 5 scaled data through arithmetic coding and Huffman coding, I obtained that arithmetic coding is better than huffman coding in processing time and compression ratio. And in case of arithmetic coding I could compress to 38% to original image data.

• ETRI Journal
• /
• v.29 no.1
• /
• pp.8-17
• /
• 2007

In this paper, we present a time domain combined field integral equation formulation (TD-CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.285-288
• /
• 1998

A least-squares identification method is studied that estimates a finite number of coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions, We will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. We show that the Laplace transform of the expansion for some sets$\Psi_{\kappa}(Z)$ is equivalent to a series expansion . Techniques based on this result are presented for obtaining the coefficients $c_{n}$ as those of a series. One of their important properties is that, if chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained.

• Proceedings of the KOSOMBE Conference
• /
• v.1996 no.05
• /
• pp.31-35
• /
• 1996

This paper presents a real time algorithm for monitoring of the arrythmia of ECG signal. A real time monitoring, following by detecting a QRS complex, is the most important. Using 2-dimensional time-delay coordinates which are reconstructed by the phase portrait plotting special trajectory, we detect QRS complexes. In this study, arrythmias are detected by matching the past standard template with tile present pattern when changing abruptly In order to matching with each other, we propose modified chain coding algorithm which applies vetor table consisting of eight orthonormal code(=binary code) to the phase portraits. This algorithm using logical function increases the weight if exceeding to the threshold determinded by correlation value and the distance from a straight line(y=x). Evaluating the performance of the proposed algorithm, we use standard MIT/BIH database. The results are fellowing, 1) Improve the speed of matching template than that of cross-correlation ever has been used. 2) Because the proposed algorithm is robust to varing fiducial point, it is possible to monitor the ECG signal with irregular RR interval. 3) In spite of baseline wandering owing to the low frequency noise, monitoring performance is not reduced.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1531-1548
• /
• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.5
• /
• pp.1054-1065
• /
• 1993

A computer simulation is performed on the effectiveness of the active minimization of harmonically excited enclosed sound fields for producing global reduction in the amplitude of the pressure fluctuations. In this study for the appreciable reductions in total time averaged acoustic potential energy, $E_{pp}$, the transducer location strategies for three dimensional active noise control is presented based on a state space modal which approximates the closed acoustic field.In this study, the above theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the used of room-like 3-dimensional rectangular enclosure it is demonstrated that the reductions in $E_{pp}$ can be achieved by using a single secondary source, provided that the source is placed within the half a wavelength from the primary source and placed away from nodal line of the sound field. Concerning the reductions in $E_{pp}$ by minimzing the pressure in sound fields by the use of 3-dimensional rectangular enclosure, the effects of the number of sensors and the locations of these sensors are investigated. When a few modes dominate the response it is found that if only a limited number of sensors are located away from nodal line and located at the pressure maxima of the sound field such as at each corner of a rectangular enclosure.