• East Asian mathematical journal
• /
• v.29 no.5
• /
• pp.467-479
• /
• 2013

We develop a Fourier-Feynman theory for Fourier-type functionals ${\Delta}^kF$ and $\widehat{{\Delta}^kF}$ on Wiener space. We show that Fourier-Feynman transform and convolution of Fourier-type functionals exist. We also show that the Fourier-Feynman transform of the convolution product of Fourier-type functionals is a product of Fourier-Feynman transforms of each functionals.

• Journal of the Optical Society of Korea
• /
• v.4 no.1
• /
• pp.54-57
• /
• 2000

Introducing left and right fractional orders separately, we show that the cascading of optical extended fractional Fourier transform systems can be easily calculated. Through such calculations we study the properties of extended fractional Fourier transforms.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.967-990
• /
• 2006

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.31B no.5
• /
• pp.26-33
• /
• 1994

Phase retrieval is concerned with the reconstruction of a signal from its Fourier transform magnitude (or intensity), which arises in many areas such as X-ray crystallography, optics, astronomy, or digital signal processing. In such areas, the Fourier transform phase of the desired signal is lost while measuring Fourier transform magnitude (F.T.M.). However, if a reference 'signal is added to the desired signal, then, in the Fourier trans form magnitude of the added signal, the Fourier transform phase of the desired signal is encoded. This paper addresses uniqueness and retrieval of the encoded Fourier phase of a multidimensional signal from the Fourier transform magnitude of the added signal along with the Fourier transform magnitude of the desired signal and the information of the additive reference signal. In Part I, several conditions under which the desired signal can be uniquely specified from the two Fourier transform magnitudes and the additive reference signal are presented. In Part II, the development of non-iterative algorithms and an iterative algorithm that may be used to reconstruct the desired signal(s) is considered.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.31B no.5
• /
• pp.34-41
• /
• 1994

Phase retrieval is concerned with the reconstruction of a signal from its Fourier transform magnitude (or intensity), which arises in many areas such as X-ray crystallography, optics, astronomy, or digital signal processing In such areas, the Fourier transform phase of the desired signal is lost while measuring Fourier transform magnitude (F.T.M.). However, if a reference 'signal is added to the desired signal, then, in the Fourier trans form magnitude of the added signal, the Fourier transform phase of the desired signal is encoded This paper addresses uniqueness and retrieval of the encoded Fourier phase of a multidimensional signal from the Fourier transform magnitude of the added signal along with Fourier transform magnitude of the desired signal and the information of the additive reference signal In Part I, several conditions under which the desired signal can be uniquely specified from the two Fourier transform magnitudes and the additive reference signal are presented In Part II, the development of non-iterative algorithms and an iterative algorithm that may be used to reconstruct the desired signal (s) is considered

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.17 no.3
• /
• pp.540-545
• /
• 2013

The Fractional Fourier transform, as a generalization of the classical Fourier Transform, was first introduced in quantum mechanics. Because of its simple and useful properties of Fractional Fourier transform in time-frequency plane, various research results in sonar and radar signal processing have been introduced and shown superior results to conventional method utilizing Fourier transform until now. In this paper, we applied Fractional Fourier transform to sonar signal processing to detect and separate the overlapping linear frequency modulated signals. Experimental results show that received overlapping LFM(Linear Frequency Modulation) signals can be detected and separated effectively in Fractional Fourier transform domain.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.609-619
• /
• 2012

In this paper we define the Fourier-type functionals via the Fourier transform on Wiener space. We investigate some properties of the Fourier-type functionals. Finally, we establish integral transform of the Fourier-type functionals which also can be expressed by other Fourier-type functionals.

• Economic and Environmental Geology
• /
• v.20 no.2
• /
• pp.119-123
• /
• 1987

Hankel transform of order 0 can be represented by a combination of Abel transform and Fourier transform. This Abel-Fourier method can offer computational advantages over a conventional digital linear filter method through the uses of a rapid Abel transform with shift variant recursive filter and of a fast Fourier transform. The Abel-Fourier method, however, is generally less accurate than a well-designed digital linear filter method. In geoelectrical applications, the digital linear filter method seems to be more flexible than the Abel-Fourier method.

• The Journal of the Acoustical Society of Korea
• /
• v.15 no.3E
• /
• pp.74-77
• /
• 1996

In this paper we implement the Discrete Rotational Fourier Transform(DRFT) which is a discrete version of the Angular Fourier Transform and its inverse transform. We simplify the computation algorithm in [4], and calculate the complexity of the proposed implementation of the DRFT and the inverse DRFT, in comparison with the complexity of a DFT (Discrete Fourier Transform).

• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.273-289
• /
• 2011

In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}$[0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.