• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.563-567
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• 2001

We generalize the widebane P0-weyl symbol (P0WS) and the widebane spreading function (WSF) using the generalized warping function . The new generalized P0WS and WSF are useful for analyzing system and communication channels producing generalized time shifts. We also investigated the relationship between the affine Wey1 symbol(AWS) and the P0WS. By using specific warping functions, we derive new P0WS and WSF as analysis tools for systems and communication channels with non-linear group delary characteristics. The new P0WS preserves specific types of changes imposed on random processes. The new WSF provides a new interpretation of output of system and communication channel as weighted superpositions of non-linear time shifts on the input. It is compared to the conventional method obtaining output of system and communication channel as a convention integration of the input with the impulse response of the system and the communication channel. The convolution integration can be interpreted as weighted superpositions of liner time shifts on the input where the weight is the impulse response of the system and the communication channel. Application examples in analysis and detection demonstrate the advantages of our new results.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.628-632
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• 2001

We propose time-frequency (TF) tools for analyzing linear time-varying (LTV) systems and nonstationary random processes. Obtained warping the narrowband Weyl symbol (WS) and spreading function (SF), the new TF tools are useful for analyzing LTV systems and random processes characterized by generalized frequency shifts, This new Weyl symbol (WS) is useful in wideband signal analysis. We also propose WS an tools for analyzing systems which produce dispersive frequency shifts on the signal. We obtain these generalized, frequency-shift covariant WS by warping conventional, narrowband WS. Using the new, generalized WS, we provide a formulation for the Weyl correspondence for linear systems with instantaneous of linear signal transformation as weighted superpositions of non-linear frequency shifts on the signal. Application examples in signal and detection demonstrate the advantages of our new results.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.5-15
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• 2005

The conharmonic transformation is a conformal trans-formation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishii and we have generalized his results. Twisted product space is a generalized warped product space with a warping function defined on a whole space. In this paper, we partially classified the twisted product space and obtain a sufficient condition for a twisted product space to be locally Riemannian products.

• Journal of the Korea Computer Graphics Society
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• v.21 no.5
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• pp.1-10
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• 2015

This study proposes a method of developing authoring tool that can easily and intuitively generate diverse digital leaves that compose virtual landscape. The main system of the proposed authoring tool consists of deformation method for the contour of leaf blade based on image warping, procedural modeling of leaf vein and visualization method based on mathematical model that expresses the color and brightness of leaves. First, the proposed authoring tool receives leaf input image and searches for contour information on the leaf blades. It then designs leaf blade deformation method that can generate diverse shapes of leaf blades in an intuitive structure using feature-based image warping. Based on the computed leaf blade contour, the system implements the generalized procedural modeling method suitable for the authoring tool that generates natural vein patterns appropriate for the leaf blade shape. Finally, the system applies visualization function that can express color and brightness of leaves and their changes over time using a mathematical model based on convolution sums of divisor functions. This paper provides texture support function so that the digital leaves that were generated using the proposed authoring tool can be used in a variety of three-dimensional digital contents field.