• Title/Summary/Keyword: Fourier transform

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LFM Signal Separation Using Fractional Fourier Transform (Fractional Fourier 변환을 이용한 LFM 신호 분리)

  • Seok, Jongwon;Kim, Taehwan;Bae, Keunsung
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.3
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    • pp.540-545
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    • 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.

Phase Retrieval Using an Additive Reference Signal: I. Theory (더해지는 기준신호를 이용한 위성복원: I. 이론)

  • Woo Shik Kim
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.31B no.5
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    • pp.26-33
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    • 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.

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Phase Retrieval Using an Additive Reference Signal: II. Reconstruction (더해지는 기준신호를 이용한 위성복원: II. 복원)

  • Woo Shik Kim
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.31B no.5
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    • pp.34-41
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    • 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

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ON UNIFORM SAMPLING IN SHIFT-INVARIANT SPACES ASSOCIATED WITH THE FRACTIONAL FOURIER TRANSFORM DOMAIN

  • Kang, Sinuk
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.613-623
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    • 2016
  • As a generalization of the Fourier transform, the fractional Fourier transform plays an important role both in theory and in applications of signal processing. We present a new approach to reach a uniform sampling theorem in the shift-invariant spaces associated with the fractional Fourier transform domain.

GENERALIZED PSEUDO-DIFFERENTIAL OPERATORS INVOLVING FRACTIONAL FOURIER TRANSFORM

  • Waphare, B.B.;Pansare, P.D.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.105-115
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    • 2021
  • Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

Implementatin of the Discrete Rotational Fourier Transform

  • Ahn, Tae-Chon
    • The Journal of the Acoustical Society of Korea
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    • v.15 no.3E
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    • pp.74-77
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    • 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).

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The Analysis of Unevenness of Spun Yarns(I) -Application of Short-Time Fourier Transform- (방적사의 불규제 해석에 관한 연구(I) -Short-Time Fourier Transform을 이용한 분석-)

  • 정성훈
    • Textile Science and Engineering
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    • v.37 no.10
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    • pp.596-602
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    • 2000
  • A new evenness evaluation method was developed in order to analyze short-termirregularity of spun yarns. The diameters of a spun yarn were measured at every 2 mm segments by using the G-580\ulcorner tester produced by Zweigle Ltd. Simultaneously, the analog signals from the instrument were captured and then converted into the digital signals with the digital signal processing system specially developed for this study by using Lab-PC+\ulcorner. In order to analyze the periodicity of the signals, Short-Time Fourier Transform(STFT) and Discrete Fourier Transform(DFT) were applied. The results from STFT were compared with those from DFT. It was found that STFT was more effective in analyzing the short-term irregularity of spun yarns than DFT and in detecting frequency content changes with time.

Study of Radix-3 FFT (Radix-3 FFT에 관한 고찰)

  • Jung, Hae-Seung
    • Aerospace Engineering and Technology
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    • v.9 no.1
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    • pp.98-105
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    • 2010
  • Fast Fourier Transform is the fast implementation of Discrete Fourier Transform, which deletes periodic operation of DFT. According to the definition, radix-2 FFT can be implemented byre cursive call which divides the input signal points into 2 signal points. Because of its time-consuming stack-copy operation, this recursive method is very slow. To overcome this drawback, butterfly operation with signal rearrangement was devised. Based on the ideas of signal rearrangement and butterfly operation, this paper applies the signal rearrangement method to the Radix-3 FFT and checks the validity of this method.

Emission Spectroscopy of Unstable Molecules using a Fourier Transform Spectrometer (Fourier Transform 분광기를 이용한 불안정한 분자의 방출분광학)

  • Sang Kuk Lee;Un Sik Kim
    • Journal of the Korean Chemical Society
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    • v.37 no.4
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    • pp.371-377
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    • 1993
  • Fourier Transform UV/VIS spectrometer has been modified for emission spectroscopy with the technique of supersonic expansion, in which the unstable molecular radical $CH_3S$ has been generated in a jet by a high voltage DC discharge. The fluorescence spectra of the supersonically cooled radical have been recorded on a Fourier Transform UV/VIS spectrometer. The ratio of signal to noise of the spectra has been improved substantially. Also the rotational structure has been clearly resolved for $CH_3S$ molecular radical.

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