• Title/Summary/Keyword: 힐버트

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Hilbert and Formalism (힐버트와 형식주의)

  • Choi, Won-Bae
    • Journal for History of Mathematics
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    • v.24 no.4
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    • pp.33-43
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    • 2011
  • In this paper I discuss if we can regard Hilbert at the time of Hilbert's program as an instrumentalist. For this I first provide some textual evidences for the instrumentalist interpretation, then examine the three recent criticisms in turn. I argue that the reading Hilbert as an instrumentalist is still tenable in spite of these criticisms.

A Study on the Hardware Complexity Reduction of Hilbert transformer by MAG algorithm (MAG 알고리즘에 의한 힐버트 변환기의 하드웨어 복잡도 감소에 관한 연구)

  • Kim, Young-Woong;Lee, Young-Seock
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.12 no.1
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    • pp.364-370
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    • 2011
  • The Hilbert transform performs a role to transform band pass signals into low pass signals in wireless communication systems. The operation of Hilbert transform is based on a convolution process which is required adding and multiplying calculations. When the Hilbert transform is designed and hardware-implemented at gate level, the adding and multiplying operation requires a high power consumption and a occupation of wide area on a chip. So the results of adding and multiplying operation cause to degrade the performance of implemented system. In this paper, the new Hilbert transformer is proposed, which has a low hardware complexity by application of MAG(Minimum Adder Graph) algorithm. The proposed Hilbert transformer was simulated in ISE environment of Xilinx and showed the reduction of hardware complexity comparing with the number of gate in the conventional Hilbert transformer.

Performance Analysis of digital phase shifter using Hilbert transform (힐버트 변환을 이용한 디지털 위상천이기의 성능 분석)

  • Seo, Sang Gyu;Jeong, Bong-Sik
    • Journal of the Institute of Convergence Signal Processing
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    • v.14 no.1
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    • pp.39-44
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    • 2013
  • In this paper digital phase-shifter for multi-arm spiral antennas was designed by using Hilbert transform. All frequency components in input signal are phase-shifted for 90 degree by Hilbert transform, and the transform is implemented by FIT and IFIT. Digital phase-shifter generates two signals with phase difference of 90 degree by using Hilbert transform from input signals sampled by analog-digital converter(ADC), and then the input signal is phase-shifted for a given phase by using two signals. Hilbert transform based on digital phase-shifter is designed by Xilinx System generator, and the effects of input noise, FIT point, sampling period, initial phase of input signal, and shifted phase are simulated and its results are compared with Matlab results.

A Study on the design of Hilbert transformer using the MAG Algorithm (MAG 알고리즘을 이용한 힐버트 변환기의 설계에 관한 연구)

  • Lee, Young-seock
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.7 no.3
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    • pp.121-125
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    • 2014
  • A hardware implementation of Hilbert transform is indespensible element in DSP system, but it suffers form a high complexity of system level hardware resulted in a large amount of the used gate. In this paper, we implemented the Hilbert transformer using MAG algorithm that reduces the complexity of hardware.

A Study on Hilbert Transform Pair of Wavelet using Truncated Coefficient Vector (절단된 계수 벡터를 사용한 웨이브렛의 힐버트 변환쌍에 관한 연구)

  • 배상범;김남호
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.7 no.5
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    • pp.1095-1100
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    • 2003
  • The wavelet transform pair used simultaneously when two wavelets are designed to form an approximate Hilbert transform pair provide excellent property than present DWT(discrete wavelet transform), especially in field that detect wide-band signals like pulse and increase the bit rate at the same bandwidth. In this paper, the two dyadic wavelet bases which form an approximate Hilbert transform pair were designed, and flat delay filter which has the truncated coefficient vector is used in order that the two filters can form Hilbert transform relation in the process of design.

Bernays and the Axiomatic Method (베르나이스와 공리적 방법)

  • Park, Woo-Suk
    • Korean Journal of Logic
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    • v.14 no.2
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    • pp.1-38
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    • 2011
  • Bernays has not drawn scholarly attention that he deserves. Only quite recently, the reevaluation of his philosophy, including the projects of editing, translating, and reissuing his writings, has just started. As a part of this renaissance of Bernays studies, this article tries to distinguish carefully between Hilbert's and Bernays' views regarding the axiomatic method. We shall highlight the fact that Hilbert was so proud of his own axiomatic method on textual evidence. Bernays' estimation of the place of Hilbert's achievements in the history of the axiomatic method will be scrutinized. Encouraged by the fact that there are big differences between the early middle Bernays and the later Bernays in this matter, we shall contrast them vividly. The most salient difference between Hilbert and Bernays will shown to be found in the problem of the uniformity of the axiomatic method. In the same vein, we will discuss the later Bernays' criticism of Carnap, for Carnap's project of philosophy of science in the late 1950's seems to be a continuation and an extension of Hilbert's faith in the uniformity of the axiomatic method.

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Implementation of 2-D Incoherent Imaging using Hilbert Transform based on Two-Pupil Optical Heterodyne Scanning System (Two-Pupil 광학 헤테로다인 스캐닝 시스템 기반의 힐버트 변환을 활용한 2-D 인코히어런트 이미징 구현)

  • Kyung, Min-Gu;Doh, Kyu-Bong
    • Journal of Advanced Navigation Technology
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    • v.16 no.2
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    • pp.240-246
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    • 2012
  • The Hilbert transform, which has been hitherto discussed in coherent imaging, is for the first time investigated in the context of incoherent imaging. Because the Hilbert transform of the information is superposed coherently with the original light field. We present a two-pupil optical heterodyne scanning system and analyze mathematically the design of its two pupils such that the optical system can perform the Hilbert transform on incoherent objects. In this paper, we review and formulate the definition of an analytic signal of a function and from which we can obtain the Hilbert transform of the function. and we analyze the design of pupils so as to obtain the Hilbert transform and show some 2-D simulations. Computer simulation results of the idea clarify the theoretical results.

Hilbert's Program as Research Program (연구 프로그램으로서의 힐버트 계획)

  • Cheong, Kye-Seop
    • Journal for History of Mathematics
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    • v.24 no.3
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    • pp.37-58
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    • 2011
  • The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.

Design and Fabrication of the GPS Receiving Antenna using Hilbert Curve Fractal Structure (힐버트 커브 프랙탈 구조를 이용한 GPS 수신 안테나 설계 및 제작)

  • Kang, Sang-Won
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.14 no.1
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    • pp.125-129
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    • 2014
  • In this paper, design and fabrication of the GPS receiving antenna using Hilbert curve fractal structure was proposed. The size of the antenna was miniaturized by transforming dipole structure into monopole structure because its size increases if Hilbert curve fractal dipole structure is used. To use a Hilbert curve structure, the current directions of the radiator were made oppositely each other. The size of the antenna is $10{\times}10{\times}0.8[mm]$, the line width is 0.25[mm]. The resonant frequency is 1.58[GHz] and its range is 1.52[GHz] ~ 1.65[GHz]. Frequency bandwidth is 130[MHz]. Antenna maximum gain is 3.09[dBi].