• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.121-131
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• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.47-54
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• 2007

In [6] some computation of spectral measures induced by normal operators $T^{*n}T^n$ was introduced. In this note we improve some computations by using spectral measures, which are related t o extremal vectors. Also, we discuss the extremal value properties and apply our spectral measure equations to moment sequences which are induced by weighted shifts.

• Korean Journal of Remote Sensing
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• v.25 no.3
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• pp.263-270
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• 2009

Noise band removal is a crucial step before spectral matching since the noise bands can distort the typical shape of spectral reflectance, leading to degradation on the matching results. This paper proposes a statistical noise band removal method for hyperspectral data using the correlation coefficient between two bands. The correlation coefficient measures the strength and direction of a linear relationship between two random variables. Considering each band of the hyperspectral data as a random variable, the correlation between two signal bands is high; existence of a noisy band will produce a low correlation due to ill-correlativeness and undirected ness. The unsupervised k-nearest neighbor clustering method is implemented in accordance with three well-accepted spectral matching measures, namely ED, SAM and SID in order to evaluate the validation of the proposed method. This paper also proposes a hierarchical scheme of combining those measures. Finally, a separability assessment based on the between-class and the within-class scatter matrices is followed to evaluate the applicability of the proposed noise band removal method. Also, the paper brings out a comparison for spectral matching measures. The experimental results conducted on a 228-band hyperspectral data show that while the SAM measure is rather resistant, the performance of SID measure is more sensitive to noise.

• The Mathematical Education
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• v.21 no.3
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• pp.25-28
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• 1983

In this paper we examine some properties of spectral measures and try to establish a fundamental theorem on the existence of the solution of a generalized Volterra equation in a Hilbert space as the results.

• Phonetics and Speech Sciences
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• v.6 no.2
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• pp.47-54
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• 2014

The purpose of this study was to analyze spectral versus cepstral measurements in esophageal speakers. The comparison between the measurements in thirteen male esophageal speakers was compared with the control group of thirteen normal speakers using the sustained vowel /a/. The main results can be summarized as below: (a) the CPP and L/H ratio of the esophageal group were significantly lower than those of the control group (b) the CPP was significantly correlated with the spectral parameters such as jitter, shimmer, NHR and VTI, and (c) the ROC analysis showed that the threshold of 10.25dB for the CPP achieved a good classification for esophageal speakers, with 100% perfect sensitivity and specificity. Thus, it was known that cepstral-based acoustic measures such as CPP, may be more reliable predictors than other spectral-based acoustic measures such as jitter and shimmer. And it was found that cepstral-based acoustic measures were effective in distinguishing esophageal voice quality from normal voice quality. This research will contribute to establishing a baseline related to speech characteristics in voice rehabilitation with laryngectomees.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.111-114
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• 2008

The existence of noise bands may deform the typical shape of the spectrum, making the accuracy of clustering degraded. This paper proposes a statistical approach to remove noise bands in hyperspectral data using the correlation coefficient of bands as an indicator. Considering each band as a random variable, two adjacent signal bands in hyperspectral data are highly correlative. On the contrary, existence of a noise band will produce a low correlation. For clustering, the unsupervised ${\kappa}$-nearest neighbor clustering method is implemented in accordance with three well-accepted spectral matching measures, namely ED, SAM and SID. Furthermore, this paper proposes a hierarchical scheme of combining those measures. Finally, a separability assessment based on the between-class and the within-class scatter matrices is followed to evaluate the applicability of the proposed noise band removal method. Also, the paper brings out a comparison for spectral matching measures.

• Computers and Concrete
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• v.16 no.5
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• pp.723-740
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• 2015

In this study, the seismic performance of skewed highway bridges has been assessed by using fragility function methodology. Incremental Dynamic Analysis (IDA) has been used to prepare complete information about the different damage states of a 30 degree skewed highway bridge. A three dimensional model of a skewed highway bridge is presented and incremental dynamic analysis has been applied. The details of the full nonlinear procedures have also been presented. Different spectral intensity measures are studied and the effects of the period on the fragility curves are shown in different figures. The efficiency, practicality and proficiency of these different spectral intensity measures are compared. A suite of 20 earthquake ground motions are considered for nonlinear time history analysis. It has been shown that, considering different intensity measures (IM) leads us to overestimate or low estimate the damage probability which has been discussed completely.

• Phonetics and Speech Sciences
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• v.6 no.3
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• pp.63-72
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• 2014

The current study assessed the utility of acoustic analyses the most commonly used in routine clinical voice assessment including perturbation, nonlinear dynamic analysis, and Spectral/Cepstrum analysis based on signal typing of dysphonic voices and investigated their applicability of clinical acoustic analysis methods. A total of 70 dysphonic voice samples were classified with signal typing using narrowband spectrogram. Traditional parameters of %jitter, %shimmer, and signal-to-noise ratio were calculated for the signals using TF32 and correlation dimension(D2) of nonlinear dynamic parameter and spectral/cepstral measures including mean CPP, CPP_sd, CPPf0, CPPf0_sd, L/H ratio, and L/H ratio_sd were also calculated with ADSV(Analysis of Dysphonia in Speech and VoiceTM). Auditory perceptual analysis was performed by two blinded speech-language pathologists with GRBAS. The results showed that nearly periodic Type 1 signals were all functional dysphonia and Type 4 signals were comprised of neurogenic and organic voice disorders. Only Type 1 voice signals were reliable for perturbation analysis in this study. Significant signal typing-related differences were found in all acoustic and auditory-perceptual measures. SNR, CPP, L/H ratio values for Type 4 were significantly lower than those of other voice signals and significant higher %jitter, %shimmer were observed in Type 4 voice signals(p<.001). Additionally, with increase of signal type, D2 values significantly increased and more complex and nonlinear patterns were represented. Nevertheless, voice signals with highly noise component associated with breathiness were not able to obtain D2. In particular, CPP, was highly sensitive with voice quality 'G', 'R', 'B' than any other acoustic measures. Thus, Spectral and cepstral analyses may be applied for more severe dysphonic voices such as Type 4 signals and CPP can be more accurate and predictive acoustic marker in measuring voice quality and severity in dysphonia.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.08a
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• pp.250-253
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• 1998

In digital communicatioin networks, speech recognition systems conventionally reconstruct speech followed by extracting feature [parameters. In this paper, we consider a useful approach by incorporating speech coding parameters into the speech recognizer. Most speech coders employed in the networks represent line spectral pairs as spectral parameters. In order to improve the recognition performance of the LSP-based speech recognizer, we introduce two different ways: one is to devise weighed distance measures of LSPs and the other is to transform LSPs into a new feature set, named a pseudo-cepstrum. Experiments on speaker-independent connected-digit recognition showed that the weighted distance measures significantly improved the recognition accuracy than the unweighted one of LSPs. Especially we could obtain more improved performance by using PCEP. Compared to the conventional methods employing mel-frequency cepstral coefficients, the proposed methods achieved higher performance in recognition accuracies.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.