• Current Optics and Photonics
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• 제7권5호
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• pp.529-536
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• 2023

The Morlet wavelet transform method is proposed to analyze a single interferogram with spatial carrier frequency that is captured by an optical interferometer. The method can retain low frequency components that contain the phase information of a measured optical surface, and remove high frequency disturbances by wavelet decomposition and reconstruction. The key to retrieving the phases from the low-frequency wavelet components is to extract wavelet ridges by calculating the maximum value of the wavelet transform amplitude. Afterwards, the wrapped phases can be accurately solved by multiple iterative calculations on wavelet ridges. Finally, we can reconstruct the wave-front of the measured optical element by applying two-dimensional discrete cosine transform to those wrapped phases. Morlet wavelet transform does not need to remove the spatial carrier frequency components manually in the processing of interferogram analysis, but the step is necessary in the Fourier transform algorithm. So, the Morlet wavelet simplifies the process of the analysis of interference fringe patterns compared to Fourier transform. Consequently, wavelet transform is more suitable for automated programming analysis of interference fringes and avoiding the introduction of additional errors compared with Fourier transform.

• 한국정보통신학회논문지
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• 제9권1호
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• pp.8-15
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• 2005

비선형적인 위상 변화를 지닌 비정상(non-stationary)신호는 레이더, 통신, 지질탐사, 음향, 생체공학 응용등 여러 분야에서 쉽게 접하는 신호이다. 비정상 신호는 일반적으로 시간의 변환에 따라 신호의 스페트럼 특성이 변화하는 신호를 의미하며, 순간 주파수는 신호의 특정시간에 해당하는 신호성분의 주파수를 의미한다. 따라서 열거한 레이더, 음향, 생ㅊ신호등에 있어서 순간 주파수는 신호의 물리적 특성을 파악하기 위한 중요한 변수이다. 이 논문에서는 연속 웨이브렛 변환을 이용한 비정상 신호의 순간 주파수를 결정에 대하여 연구하였고, 기존의 방법과 비교하였다. 신호에 잡음이나 여러 가지의 주파수가 중첩되어 있는 경우, 기존에 방법들로서는 정확한 순간 주파수를 결정할 수 없는 반면, 웨이브렛 변환을 이용한 경우, 신호의 성분에 관계없이 상당히 정확한 순간주파수를 결정할 수 있음에 대하여 설명하였다.

• Wind and Structures
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• 제20권5호
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• pp.661-682
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• 2015

This study investigates the use of time-frequency coherence analysis for detecting and evaluating coherent "structures" of surface pressures and wind turbulence components, simultaneously on the time-frequency plane. The continuous wavelet transform-based coherence is employed in this time-frequency examination since it enables multi-resolution analysis of non-stationary signals. The wavelet coherence quantity is used to identify highly coherent "events" and the "coherent structure" of both wind turbulence components and surface pressures on rectangular prisms, which are measured experimentally. The study also examines, by proposing a "modified" complex Morlet wavelet function, the influence of the time-frequency resolution and wavelet parameters (i.e., central frequency and bandwidth) on the wavelet coherence of the surface pressures. It is found that the time-frequency resolution may significantly affect the accuracy of the time-frequency coherence; the selection of the central frequency in the modified complex Morlet wavelet is the key parameter for the time-frequency resolution analysis. Furthermore, the concepts of time-averaged wavelet coherence and wavelet coherence ridge are used to better investigate the time-frequency coherence, the coherently dominant events and the time-varying coherence distribution. Experimental data derived from physical measurements of turbulent flow and surface pressures on rectangular prisms with slenderness ratios B/D=1:1 and B/D=5:1, are analyzed.

• Journal of Mechanical Science and Technology
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• 제20권12호
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• pp.2147-2158
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• 2006

The continuous wavelet transform (CWT) has a frequency-adaptive time-frequency tiling property, which makes it popular for the analysis of dispersive elastic wave signals. However, because the time-frequency tiling of CWT is not signal-dependent, it still has some limitations in the analysis of elastic waves with spectral components that are dispersed rapidly in time. The objective of this paper is to introduce an advanced time-frequency analysis method, called the dispersion-based continuous wavelet transform (D-CWT) whose time-frequency tiling is adaptively varied according to the dispersion relation of the waves to be analyzed. In the D-CWT method, time-frequency tiling can have frequency-adaptive characteristics like CWT and adaptively rotate in the time-frequency plane depending on the local wave dispersion. Therefore, D-CWT provides higher time-frequency localization than the conventional CWT. In this work, D-CWT method is applied to the analysis of dispersive elastic waves measured in waveguide experiments and an efficient procedure to extract information on the dispersion relation hidden in a wave signal is presented. In addition, the ridge property of the present transform is investigated theoretically to show its effectiveness in analyzing highly time-varying signals. Numerical simulations and experimental results are presented to show the effectiveness of the present method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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• pp.114-116
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• 2006

This paper is to propose the palm print recognition system using wavelet transform. The palm print is frequently used as the material for the biometric recognition system such as the finger print, iris, face, etc. Since the palm print has lots of properties which include principle line, wrinkles, ridge and so forth, the ways of the implementation of the system are various. In this paper, at first, the palm print image is acquired and then some level of wavelet transform is performed. The coefficients become to be some blocks size of M by N after divided into the horizontal, vertical, diagonal components each level. The mean values, which are calculated with values of each block, are used as the feature vector. To compare between the stored template and the acquired vectors, we adopt the PNN (Probability Neural Network) method.

• Smart Structures and Systems
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• 제22권3호
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• pp.359-368
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• 2018

A method is proposed for the identification of instantaneous frequencies (IFs) in time-varying structures. The proposed method combines a maximum gradient algorithm and a smoothing operation. The maximum gradient algorithm is designed to extract the wavelet ridges of response signals. The smoothing operation, based on a polynomial curve fitting algorithm and a threshold method, is employed to reduce the effects of random noises. To verify the effectiveness and accuracy of the proposed method, a numerical example of a signal with two frequency modulated components is investigated and an experimental test on a steel cable with time-varying tensions is also conducted. The results demonstrate that the proposed method can extract IFs from the noisy multi-component signals and practical response signals successfully. In addition, the proposed method can provide a better IF identification results than the standard synchrosqueezing wavelet transform.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.583-594
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• 2021

In this paper, we propose wavelet-based procedures to identify the difference between images, including portraits and handwriting. The proposed methods are based on a novel combination of multiscale methods with a regularization technique. The multiscale method extracts the local characteristics of an image, and the distinct features are obtained through the regularized regression of the local characteristics. The regularized regression approach copes with the high-dimensional problem to build the relation between the local characteristics. Lytle and Yang (2006) introduced the detection method of forged handwriting via wavelets and summary statistics. We expand the scope of their method to the general image and significantly improve the results. We demonstrate the promising empirical evidence of the proposed method through various experiments.