• 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.

• 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

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.11C
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• pp.1060-1067
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• 2005

In this paper, we generalize the shift-invariance properties of linear time-frequency distributions to the fractional Fourier domains that interpolate between the time and frequency domains. Magnitude-wise shift invariance in arbitrary fractional Fourier domains distinguishes the short-time Fourier transform (STFT) among all linear time-frequency distributions and simplifies the interpretation of the resultant distribution. We prove that the STFT is the only linear distribution that satisfies the magnitude-wise shift-invariance property in the fractional Fourier domains.

• The Journal of the Acoustical Society of Korea
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• v.37 no.6
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• pp.518-524
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• 2018

The cover song refers to live recordings or reproduced albums. This paper studies two-dimensional Fourier transform as a feature-dimension reduction method to search cover song fast. The two-dimensional Fourier transform is conducive in feature-dimension reduction for cover song search due to musical-key invariance. This paper extends the previous work, which only utilize the magnitude of the Fourier transform, by introducing an invariant from phase based on the assumption that adjacent frames have the same musical-key change. We compare the cover song retrieval accuracy of the Fourier-transform based methods over two datasets. The experimental results show that the addition of the invariant from phase improves the cover song retrieval accuracy over the previous magnitude-only method.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.3
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• pp.60-67
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• 2009

The phase retrieval problem is a problem of reconstructing a signal or the phase of Fourier transform of the signal from the magnitude of its Fourier transform. In this paper we address the problem of reconstructing an unknown signal from the magnitude of its Fourier transform and the magnitude of Fourier transform of another signal that is given by the addition of the desired signal. After we briefly mention the uniqueness conditions under which a signal can be uniquely specified from the given information and key equations of the iterative algorithm, we present mathematical background that the iterative algorithm converges to the desired signal, present an example that illustrates the performance of the reconstruction algorithm, and show its convergence property.

• Journal of the Korean Ceramic Society
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• v.36 no.2
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• pp.122-129
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• 1999

Alumina tapes, having various weight ratios of alumina powder/(alumina+binder+plasticizer), X, and binder / (binder+plsticizer), Y, were prepared and their complex modulus was measured using Micro Fourier Rheometer. As the X and Y ratios increased, Transfer function(TF) magnitude and Transfer function (TF) phase increased and decreased, respectively, indicating that the elastic modulus of the tapes depends on the weight ratios. The temperature dependence of the viscosity of the tapes was visualized by the decreased TF magnitude and the increased TF phase. The Y ratio dependence of the complex modulus related to the glass transition temperature of the tapes and the moduls change by the Y ratio was higher than that by the X ratio within the comperature of the tapes and the modulus changes by the Y ratio was higher than that by the X ratio within the composition range, investigated in the present study. The measurement of the complex modulus of the alumina tapes suggested that the TF phase should be higher that 17$^{\circ}$for the tapes to be utilized for 3-dimensional shaping.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1078-1086
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• 2009

This paper presents a Fourier based algorithm for estimating the parameters of the low frequency oscillating modes. The proposed methods estimates various parameters(frequency, damping factor, mode magnitude, phase) by fitting Fourier spectrum and phase with a damped exponential cosine function. Dominant frequency is selected by taking frequency corresponding to the peak spectrum, and damping factor is estimated using the left/right spectra of Fourier spectrum. In addition, mode magnitude is calculated by the normalized peak spectrum, and phase is estimated from spectrum phase. Also, we introduce an accuracy index in order to determine the accuracy of the estimated parameters, and the index is calculated using the deviations of the peak spectrum and the left/right spectra. The parameter estimation methods proposed in this paper include very simple arithmetical processes, so the algorithms are simple and the calculation speed is very fast. The proposed methods are applied to test functions with two dominant modes. The results show that the proposed methods are highly applicable to low frequency parameter estimation.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.1
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• pp.105-114
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• 1997

The phase retrieval problem is concerned with the reconstruction of a signal or its fourier transform phase form the fourier transform magnitude of the signal. This problem does not have a unique solution, in general. If, however, the desired signal is minimum-phase, then it can be decided uniquely. This paper shows that we can make a minimum-phase signal by adding a delta function having a large value at the origin of an arbitrary one-dimensional signal, and a two-dimensional signal can be uniquely specified from its fourier transform magnitude if it is added by a delta function having a large value at the origin, and finally we can solve a two-dimensional phase retrieval problem by decomposing it into several ine-dimensional phase retrieval problems.

• Proceedings of the Acoustical Society of Korea Conference
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• spring
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• pp.195-198
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• 2002

This paper presents an improved MELP Coder using Fourier magnitude compensation method chosen the new 2.4 kbit/s U.S. federal Standard. Although the MELP is quite good, it has some distortion for low-pitch male speakers. An improved MELP coder includes a post processing for the fourier magnitude model that allows the MELP to reconstruct the lower frequency spectrum more accurately and improve the speech quality. In this new compensation algorithm, the harmonic magnitudes in the low frequencies are adaptively modified by removing the effect of the two filters. Also, the bit rate of the improved MELP coder is the same as that of the Federal Standard MELP coder. formal quality tests show that the improved MELP coder was preferred over the Federal Standard MELP coder by $80.8\%$.

• The Transactions of the Korean Institute of Power Electronics
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• v.16 no.3
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• pp.234-241
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• 2011

This paper proposes a simple static overmodulation strategy that extends the linearity of the inverter output voltage. The proposed method obtains the reference vector having the instantaneous value directly from the modulation index based on the magnitude of fundamental voltage, and has a simplified form of phase command. This method does not need trigonometric functions for calculating the magnitude of the reference vector. The magnitude of reference voltage and holding angle in the overmodulation region corresponding to the modulation index are determined in advance to have the same fundamental voltage magnitude by using the result of Fourier series expansion.