• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.1057-1063
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• 1994

An instantaneous frequency analysis is a technique to examine a signature for the rotating machinery if the signal has several transitions within a cycle. This paper discusses the conditions of existing negative frequency components in the instantaneous frequency. By using a signal consisted of two frequency components, the instantaneous frequency analysis is conducted while the amplitude ratio between two frequency components has been changed. The analysis shows that, depending on the amplitude ratio, the instantaneous frequencies have averaged, zero-valued, or negative components. It turns out that the negative-valued instantaneous frequencies, which have been regarded as the noise effect, are the consequence of the calculation process for the multisignal components. The criteria of existing the negative values in instantaneous frequencies is given in terms of the relative amplitude ratio and the frequency difference. Especially when the amplitude ratio approaches to 1, the instantaneous frequency fluctuates ${\pm}\infty$ in theory, which implies that instantaneous frequency has unstable region around the amplitude ratio, 1.Also, as the frequency difference between major signal components is increased, the region of existing negative instantaneous becomes broader. In an instantaneous frequency analysis, therefore, a narrow band analysis is suggested, with extreme care if the amplitude ratio approaches to 1. In this paper, a vibration signal monitored from a rotating machinery is also examined as an application example in order to show the existence of negative instantaneous frequencies components.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.162-166
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• 2012

The instantaneous amplitude (IA) based on the higher order differential energy operator is proposed. And its general form for arbitrary order is also proposed. The various definitions of the IA and the instantaneous frequency (IF) estimators are considered. The IA and IF estimators based on the energy operators need less computational cost than the conventional IF and IA estimators exploiting the Hilbert transform. The IF and IA estimators are compared in terms of the frequency and amplitude tracking accuracy of the AM-FM signals. For noiseless case, the IA and IF estimators based on the Teager-Kaiser energy operator show better tracking performance than the IF and IA estimators based on the higher energy operators. However, under noisy condition, the IF and IA estimator based on the higher order energy operators with the order 3 and 4 show better tracking than the Teager-Kaiser energy based estimators. The IF and IA estimators are applied to signals in the various power anomalies to show their usefulness as the disturbance detectors.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.8
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• pp.1193-1198
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• 2012

An instantaneous amplitude (IA) estimator using the symmetric higher order differential energy operator is proposed. The amplitude estimator and the instantaneous frequency (IF) estimator based on the symmetric higher order differential energy operator coincide with the analyzed signal in time, and they show better estimation results than the IA and IF based on the higher order differential energy operator. Various IF and IA estimators are applied to AM-FM signals for the performance comparison. Among the IF and IA estimators, the IF and IA estimators based on the symmetric higher order energy operator show the best estimation accuracy. Then, the IA and IF estimators are applied to the distorted power line signal to show their usefulness as power disturbance detectors.

• Smart Structures and Systems
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• v.33 no.6
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• pp.385-398
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• 2024

To improve the accuracy of time-frequency analysis (TFA) and instantaneous frequency (IF) extraction of structural dynamic response signals, this paper improves the spline-kernelled chirplet transform, and a new form of modified spline-kernelled chirplet transform (MSCT) based on revised Gaussian window function and energy concentration principle is put forward. The effectiveness of the proposed method is verified by numerical examples of single-component signal, multicomponent signal, single-degree-of-freedom Duffing nonlinear system and two-layer shear frame structure model. Then, a time-varying cable test is designed to collect the acceleration response signals under linear changing tension, and the IF extraction of these signals is performed by using MSCT, which further verifies the effectiveness and accuracy of this method. Through numerical simulation and experimental verification, it is proved that the proposed method can effectively extract the IF of nonlinear structure and time-varying structure.

• Journal of Biomedical Engineering Research
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• v.31 no.6
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• pp.417-426
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• 2010

We present a speech processing strategy incorporating instantaneous frequency (IF) encoding for the enhancement of melody recognition performance of cochlear implants. For the IF extraction from incoming sound, we propose the use of a Teager energy operator (TEO), which is advantageous for its lower computational load. From time-frequency analysis, we verified that the TEO-based method provides proper IF encoding of input sound, which is crucial for melody recognition. Similar benefit could be obtained also from the use of a Hilbert transform (HT), but much higher computational cost was required. The melody recognition performance of the proposed speech processing strategy was compared with those of a conventional strategy using envelope extraction, and the HT-based IF encoding. Hearing tests on normal subjects were performed using acoustic simulation and a musical contour identification task. Insignificant difference in melody recognition performance was observed between the TEO-based and HT-based IF encodings, and both were superior to the conventional strategy. However, the TEO-based strategy was advantageous considering that it was approximately 35% faster than the HT-based strategy.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.3 s.303
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• pp.99-106
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• 2005

Instantaneous Frequency(IF) of Doppler signals is used to get the information of relative velocity and miss distance between a missile and the corresponding target. Though Short-Time Fourier Transform(STFT) is mainly used to estimate IF, it has many errors in wide band signals where frequency changes sharply. Because it has a fixed window in time and frequency axes. This paper deals with IF estimation of Doppler signal using a Continuous Wavelet Transform(CWT) which has adaptive window in time and frequency axes. The proposed method is able to estimate IF regardless of frequency changes because it has a narrow window in high frequency band and a wide window in low frequency band. The experimental results demonstrate that the proposed method outperforms STFT in estimating IF.

• Smart Structures and Systems
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• v.33 no.3
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• pp.201-215
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• 2024

Spline chirplet transform and local maximum synchrosqueezing are introduced to present a novel structural instantaneous frequency (IF) identification method named local maximum synchrosqueezing spline chirplet transform (LMSSSCT). Namely spline chirplet transform (SCT), a transform is firstly introduced based on classic chirplet transform and spline interpolated kernel function. Applying SCT in association with local maximum synchrosqueezing, the LMSSSCT is then proposed. The index of accuracy and Rényi entropy show that LMSSSCT outperforms the other time-frequency analysis (TFA) methods in processing analytical signals, especially in the presence of noise. Numerical examples of a Duffing nonlinear system with single degree of freedom and a two-layer shear frame structure with time-varying stiffness are used to verify the effectiveness of structural IF identification. Moreover, a nonlinear supported beam structure test is conducted and the LMSSSCT is utilized for structural IF identification. Numerical simulation and experimental results demonstrate that the presented LMSSSCT can effectively identify the IFs of nonlinear structures and time-varying structures with good accuracy and stability.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.643-649
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• 1999

In this paper, we proposed that ｉ) noise-tolerant four kinds of AM(Amplitude Modulation)-FM(Frequency Modulation) demodulators are designed, ⅱ) we derived undersampling frequency through the product via energy operator of the monocomponent AM-FM signals separated form two-component AM-FM signals, and ⅲ) these four kinds of AM-FM demodulators detect respectively information signals of the IA(Instantaneous Amplitude) and IF(Instantaneous Frequency) by undersampling frequency to be different each other from the undersampled monocomponet AM-FM signals. Particularly, the proposed algorithm can control undersampling frequency by an integer factor. And these efficient AM-FM demodulators are well worked with the undersampled AM-FM signals.

• Journal of Korean Association for Spatial Structures
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• v.20 no.2
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• pp.77-85
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• 2020

This paper examined the dynamic instability of a shallow arch according to the response characteristics when nearing critical loads. The frequency changing feathers of the time-domain increasing the loads are analyzed using Fast Fourier Transformation (FFT), while the response signal around the critical loads are analyzed using Hilbert-Huang Transformation (HHT). This study reveals that the models with an arch shape of h = 3 or higher exhibit buckling, which is very sensitive to the asymmetric initial conditions. Also, the critical buckling load increases as the shape increases, with its feather varying depending on the asymmetric initial conditions. Decomposition results show the decrease in predominant frequency before the threshold as the load increases, and the predominant period doubles at the critical level. In the vicinity of the critical level, sections rapidly manifest the displacement increase, with the changes in Instantaneous Frequency (IF) and Instant Energy (IE) becoming apparent.

• Journal of IKEEE
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• v.24 no.4
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• pp.1081-1085
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• 2020

Instantaneous frequencies (IF) of the AM-FM signal is estimated based on the inflection point detection (IPD) method. Local maxima/minima are detected using the IPD, and they are exploited to find the IF of AM and FM components, respectively. The envelope of the maxima/minima is obtained to estimate the IF of the AM part. And the distance between neighboring maxima (or minima) is used to estimate the IF of the FM component. Computer simulation shows that the proposed method properly estimates the IF of the AM and FM when the signal has fixed frequencies for both parts. In the case of the time-varying IF of the FM part, the estimated IF shows some deviation from the true IF due to the rough sampling effect of the maximum/minimum points. Thus, the post-processing such as the lowpass filtering of the estimated IF is required to refine the resulting IF estimation.