• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.215-225
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• 2017

In this paper, we study some equivalence relations between continuous frames in a Hilbert space ${\mathcal{H}}$. In particular, we seek two necessary and sufficient conditions under which two continuous frames are near. Moreover, we investigate a distance between continuous frames in order to acquire the closest and nearest tight continuous frame to a given continuous frame. Finally, we implement these results for shearlet and wavelet frames in two examples.

• The Journal of the Acoustical Society of Korea
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• v.17 no.2E
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• pp.31-37
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• 1998

This paper proposes a feature extraction method using wavelet transform for speech recognition. Speech recognition system generally carries out the recognition task based on speech features which are usually obtained via time-frequency representations such as Short-Time Fourier Transform (STFT) and Linear Predictive Coding(LPC). In some respects these methods may not be suitable for representing highly complex speech characteristics. They map the speech features with same may not frequency resolutions at all frequencies. Wavelet transform overcomes some of these limitations. Wavelet transform captures signal with fine time resolutions at high frequencies and fine frequency resolutions at low frequencies, which may present a significant advantage when analyzing highly localized speech events. Based on this motivation, this paper investigates the effectiveness of wavelet transform for feature extraction of wavelet transform for feature extraction focused on enhancing speech recognition. The proposed method is implemented using Sampled Continuous Wavelet Transform (SCWT) and its performance is tested on a speaker-independent isolated word recognizer that discerns 50 Korean words. In particular, the effect of mother wavelet employed and number of voices per octave on the performance of proposed method is investigated. Also the influence on the size of mother wavelet on the performance of proposed method is discussed. Throughout the experiments, the performance of proposed method is discussed. Throughout the experiments, the performance of proposed method is compared with the most prevalent conventional method, MFCC (Mel0frequency Cepstral Coefficient). The experiments show that the recognition performance of the proposed method is better than that of MFCC. But the improvement is marginal while, due to the dimensionality increase, the computational loads of proposed method is substantially greater than that of MFCC.

• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.1087-1107
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• 2016

A method of damage detection based on the moving harmonic excitation and continuous wavelet transforms is presented. The applied excitation is used as a moving actuator and its frequency and speed parameters can be adjusted for an amplified response. The continuous wavelet transforms, CWT, is used for cracks detection based on the resulting amplified signal. It is demonstrated that this identification procedure is largely better than the classical ones based on eigenfrequencies or on the eigenmodes wavelet transformed. For vibration responses, free and forced vibration analyses of multi-cracked beams are investigated based on both analytical and numerical methodological approaches. Cracks are modeled through rotational springs whose compliances are evaluated using linear elastic fracture mechanics. Based on the obtained forced responses, multi-cracks positions are accurately identified and the CWT identification can be highly improved by adjusting the frequency and the speed excitation parameters.

• Smart Structures and Systems
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• v.1 no.2
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• pp.185-215
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• 2005

Advanced signal processing techniques have been long introduced and widely used in structural health monitoring (SHM) and nondestructive evaluation (NDE). In our research, we applied several signal processing approaches for our embedded ultrasonic structural radar (EUSR) system to obtain improved damage detection results. The EUSR algorithm was developed to detect defects within a large area of a thin-plate specimen using a piezoelectric wafer active sensor (PWAS) array. In the EUSR, the discrete wavelet transform (DWT) was first applied for signal de-noising. Secondly, after constructing the EUSR data, the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used for the time-frequency analysis. Then the results were compared thereafter. We eventually chose continuous wavelet transform to filter out from the original signal the component with the excitation signal's frequency. Third, cross correlation method and Hilbert transform were applied to A-scan signals to extract the time of flight (TOF) of the wave packets from the crack. Finally, the Hilbert transform was again applied to the EUSR data to extract the envelopes for final inspection result visualization. The EUSR system was implemented in LabVIEW. Several laboratory experiments have been conducted and have verified that, with the advanced signal processing approaches, the EUSR has enhanced damage detection ability.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.32 no.5
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• pp.14-25
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• 2000

In this investigation, a wavelet transform analysis was used to decompose beta-radiographic formation images into spectral and spatial components. Conventional formation analysis may use spectral analysis, based on Fourier transformation or variance vs. zone size, to describe the grammage distribution of features such as flocs, streaks and mean fiber orientation. However, these methods have limited utility for the analysis of statistically stationary data sets where variance is not uniform with position, e.g. paper machine CD profiles (especially those that contain streaks). A continuous wavelet transform was used to analyze formation data arrays obtained from radiographic imaging of handsheets and cross machine paper samples. The response of the analytical method to grammage, floc size distribution, mean fiber orientation an sensitivity to feature localization were assessed. From wavelet analysis, the change in scale of grammage variation as a function of position was used to demonstrate regular and isolated differences in the formed structure.

• Earthquakes and Structures
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• v.3 no.6
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• pp.839-852
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• 2012

Earthquake records are often analyzed in various earthquake engineering problems, making time-frequency analysis for such records of primary concern. The best tool for such analysis appears to be based on wavelet functions; selection of which is not an easy task and is commonly carried through trial and error process. Furthermore, often a particular wavelet is adopted for analysis of various earthquakes irrespective of record's prime characteristics, e.g. wave's magnitude. A wavelet constructed based on records' characteristics may yield a more accurate solution and more efficient solution procedure in time-frequency analysis. In this study, a low-pass reconstruction filter is obtained for each earthquake record based on multi-resolution decomposition technique; the filter is then assigned to be the normalized version of the last approximation component with respect to its magnitude. The scaling and wavelet functions are computed using two-scale relations. The calculated wavelets are highly efficient in decomposing the original records as compared to other commonly used wavelets such as Daubechies2 wavelet. The method is further advantageous since it enables one to decompose the original record in such a way that a clear time-frequency resolution is obtained.

• Journal of Korea Society of Digital Industry and Information Management
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• v.10 no.3
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• pp.237-247
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• 2014

This paper describes a 2D discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor, Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The TQWT can also be used as an easily-invertible discrete approximation of the continuous wavelet transform. The transform is based on a real valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e. g. 3-4 times overcomplete) being sufficient for the analysis/synthesis functions to be well localized. Therefore, This method services good performance in image processing fields.

• Journal of the Korean Society for Nondestructive Testing
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• v.21 no.1
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• pp.54-61
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• 2001

A software package to classify acoustic emission (AE) signals using the wavelet transform and the neural network was developed Both of the continuous and the discrete wavelet transforms are considered, and the error back-propagation neural network is adopted as m artificial neural network algorithm. The signals acquired during the 3-point bending test of specimens which have artificial defects on weld zone are used for the classification of the defects. Features are extracted from the time-frequency plane which is the result of the wavelet transform of signals, and the neural network classifier is tamed using the extracted features to classify the signals. It has been shown that the developed software package is useful to classify AE signals. The difference between the classification results by the continuous and the discrete wavelet transforms is also discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.176-181
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• 2002

The continuous Gabor wavelet transform (GWT) has been utilized as a useful time-frequency analysis tool to identify the rapidly-varying characteristics of some wave signals. In the application of GWT, it is important to select the Gabor wavelet with the optimal shape factor by which the time-frequency distribution of a signal can be accurately estimated. To find the signal-dependent optimal Gabor wavelet shape factor, the notion of the Shannon entropy which mesures the extent of signal energy concentration in the time-frequency plane is employed. To verify the validity of the present entropy-based scheme, we have applied it to the time-frequency analysis of a set of elastic bending wave signals generated by an impact in a solid cylinder.

• Structural Engineering and Mechanics
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• v.38 no.1
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• pp.81-97
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• 2011

In this research, the wavelet transform is used to analyze time response of a cracked beam carrying moving mass for damage detection. In this respect, a new damage detection method based on the combined use of continuous and discrete wavelet transforms is proposed. It is shown that this method is more capable in making damage signature evident than the traditional two approaches based on direct investigation of the wavelet coefficients of structural response. By the proposed method, it is concluded that strain data outperforms displacement data at the same point in revealing damage signature. In addition, influence of moving mass-induced terms such as gravitational, Coriolis, centrifuge forces, and pure inertia force along the deflection direction to damage detection is investigated on a sample case. From this analysis it is concluded that centrifuge force has the most influence on making both displacement and strain data damage-sensitive. The Coriolis effect is the second to improve the damage-sensitivity of data. However, its impact is considerably less than the former. The rest, on the other hand, are observed to be insufficient alone.