• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.569-579
• /
• 1997

We investigate the existence of the operator-valued Feynman integral when a Wiener functional is given by a Fourier transform of complex Borel measure.

• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.541-555
• /
• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• Speech Sciences
• /
• v.10 no.2
• /
• pp.77-84
• /
• 2003

In this research, we seek the beginning of the speech and detect the stationary speech region using lip information. Performing running average of the estimated speech signal in the stationary region, we reduce the effect of musical noise which is inherent to the conventional MlMSE (Minimum Mean Square Error) speech enhancement algorithm. In addition to it, SFM (Spectral Flatness Measure) is incorporated to reduce the speech signal estimation error due to speaking habit and some lacking lip information. The proposed algorithm with Wiener filtering shows the superior performance to the conventional methods according to MOS (Mean Opinion Score) test.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.133-146
• /
• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• Journal of applied mathematics & informatics
• /
• v.7 no.3
• /
• pp.959-968
• /
• 2000

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measure [1]. In this paper, I investigate a stability of the Feynman integral with respect to the potentials.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.179-200
• /
• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.151-158
• /
• 1989

Let (H, B, .nu.) be an abstract Wiener space where H is a separable Hilbert space with the inner product <.,.> and the norm vertical bar . vertical bar=.root.<.,.>, which is densely and continuously imbedded into a separable Banach space B with the norm ∥.∥ , and .nu. is a probability measure on the Borel .sigma.-algebra B(B) of B which satisfies (Fig.) where $B^{*}$ is the topological dual of B and (.,.) is the natural dual pairing between B and $B^{*}$. We will regard $B^{*}$.contnd.H.contnd.B in the natural way. Thus we have =(y, x) for all y in $B^{*}$ and x in H. Let $R^{n}$ and C denote the n-dimensional Euclidean space and the complex numbers respectively.ctively.

• Journal of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1065-1082
• /
• 2012

In this paper we first investigate the existence of the generalized Fourier-Feynman transform of the functional F given by $$F(x)={\hat{\nu}}((e_1,x)^{\sim},{\ldots},(e_n,x)^{\sim})$$, where $(e,x)^{\sim}$ denotes the Paley-Wiener-Zygmund stochastic integral with $x$ in a very general function space $C_{a,b}[0,T]$ and $\hat{\nu}$ is the Fourier transform of complex measure ${\nu}$ on $B({\mathbb{R}}^n)$ with finite total variation. We then define two sequential transforms. Finally, we establish that the one is to identify the generalized Fourier-Feynman transform and the another transform acts like an inverse generalized Fourier-Feynman transform.

• 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 Broadcast Engineering
• /
• v.18 no.3
• /
• pp.455-462
• /
• 2013

This paper introduces the Spatially Preprocessed Speech Distortion Weighted Multi-channel Wiener Filter (SP-SDW-MWF) for multi-microphone noise reduction and proposes a method to determine the speech distortion weights. The SP-SDW-MWF is known as a robust noise reduction algorithm against the error caused by the mismatch in microphones. The SP-SDW-MWF adopts weights which determine the amount of noise reduction at the expense of introducing speech distortion in the noise-suppressed speech. In this paper, we use the error of power spectral density between the estimated signal and the desired signal as the evaluation measure. Thus the a priori SNR is used to control the speech distortion weights in the frequency domain. In the experimental results, the proposed method yields better result in terms of MFCC distortion compared to the conventional method.