• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.312-317
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• 1999

An inflection point on a curve is a point where the curvature vanishes. An inflection point is useful for various geometric operations such as the approximation of curves and intersection points between curves or curve approximations. An inflection point on planar Bezier curves can be easily detected using a hodograph and a derivative of hodograph, since the closed from of hodograph is known. In the case of rational Bezier curves, for the detection of inflection point, it is needed to use the first and the second derivatives have higher degree and are more complex than those of non-rational Bezier curvet. This paper presents three methods to detect inflection points of rational Bezier curves. Since the algorithms avoid explicit derivations of the first and the second derivatives of rational Bezier curve to generate polynomial of relatively lower degree, they turn out to be rather efficient. Presented also in this paper is the theoretical analysis of the performances of the algorithms as well as the experimental result.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.562-565
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• 2013

A new variable rate speech coding technique is proposed. The method is based on the observation that the speech signal approximately looks linear for a very short period of time. The information transmitted is the location and data value of inflection points. If the distance between the inflection points is large, the mid point location and its data value are also delivered. Thus, the encoder transmits both the location and the data value for the inflection samples, but the location only for the non-inflection points. The location information is expressed using one bit for each sample, 0 for non-inflection and 1 for inflection point. At the receiver, using the interpolation, the decoder estimates the untransmitted sample values for non-inflection locations from the received sample values for the inflection samples. With 50 % of computational cost of the existing CVSD delta modulation, the proposed method is expected to achieve the data rate of 36 to 38 kbps and the SNR of 10 to 13 dB.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.12
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• pp.1750-1754
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• 2013

A variable bit rate speech coder is presented. The coder is based on the observation that a speech signal can be viewed as a combination of piecewise linear signals in a short time period. The encoder detects the sample points where the slope of the signal changes, which are called the inflection points in this paper. The coder transmits the location and value for the detected inflection sample, but only the location information for the noninflection samples. In the decoder, the noninflection samples are estimated with interpolation of the received information. Several factors affecting the performance of the coder have been tested through simulation. Simulation results show that the linear interpolation produces 1 ~ 5 dB improvement over the cubic spline interpolation. And the -law companding does not provide any benefit when it is applied before the inflection detection. With low threshold values in the inflection point detection, the coder shows better MOS and more than 16 dB improvement in SNR compared to the continuously variable slope delta modulation (CVSDM).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.4
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• pp.300-304
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• 2015

A low bit rate speech coder based on the non-uniform sampling technique is proposed. The non-uniform sampling technique is based on the detection of inflection points (IP). A speech block is processed by the IP detector, and the detected IP pattern is compared with entries of the IP database. The address of the closest member of the database is transmitted with the energy of the speech block. In the receiver, the decoder reconstructs the speech block using the received address and the energy information of the block. As results, the coder shows fixed data rate contrary to the existing speech coders based on the non-uniform sampling. Through computer simulation, the usefulness of the proposed technique is shown. The SNR performance of the proposed method is approximately 5.27 dB with the data rate of 1.5 kbps.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.4
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• pp.276-280
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• 2016

A fixed rate speech coder based on the filter bank and the non-uniform sampling technique is proposed. The non-uniform sampling is achieved by the detection of inflection points (IPs). A speech block is band passed by the filter bank, and the subband signals are processed by the IP detector, and the detected IP patterns are compared with entries of the IP database. For each subband signal, the address of the closest member of the database and the energy of the IP pattern are transmitted through channel. In the receiver, the decoder recovers the subband signals using the received addresses and the energy information, and reconstructs the speech via the filter bank summation. As results, the coder shows fixed data rate contrary to the existing speech coders based on the non-uniform sampling. Through computer simulation, the usefulness of the proposed technique is confirmed. The signal-to-noise ratio (SNR) performance of the proposed method is comparable to that of the uniform sampled pulse code modulation (PCM) below 20 kbps data rate.

• Journal of IKEEE
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• v.25 no.4
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• pp.710-715
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• 2021

Power line signal can show disturbances due to various causes. Typical anomalies are temporary sag/swell of the amplitude, flat topped signal, and harmonic distortions. The disturbances need to be detected and treated properly for the quality of the power signal. In this study, the power disturbances are detected using the inflection points (IP). The inflection points are defined as points where local maxima/minima or the slope changes occur. The power line signal has a fixed IP pattern since it is basically sinusoidal, and it may have additional inflection points if there is any disturbance. The disturbance is detected by comparing the IP patterns between the normal signal and distorted signal. In addition, by defining a cost function, the time instant where the disturbance happens can be decided. The computer simulation shows that the proposed method is useful for the detection of various disturbances. The simple sag or swell signal only shows the amplitude changes at the detected inflection points. However, the flat top signal and harmonically distorted signal produce additional inflection points and large values in the cost function. These results can be exploited for the further processing of disturbance classification.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.4 s.304
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• pp.127-132
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• 2005

The curve of motion indicated to waveform of the fast movement of human extracted using virtual reality or the quantity of time fluctuation of the electromagnetic signal as the quantity of electric fluctuation of the atmosphere is complex. It is important to decide exactly the signal property as the inflection point for the observation signal. When the signal is mixed by noise signal, the traditional method is difficult to detect the inflection point. In this paper the noisy signal is eliminated by wavelet thresholding method and the filter using natural observation theorem is applied. It shows that the inflection point of the signal waveform can be detected exactly.

• Journal of IKEEE
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• v.27 no.4
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• pp.472-476
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• 2023

Fundamental frequency/pitch period are major characteristics of speech signals. They are used in many speech applications like speech coding, speech recognition, speaker identification, and so on. In this paper, some of inflection points are used to estimate the pitch which is the inverse of the fundamental frequency. The inflection points are defined as points where local maxima, local minima or the slope changes occur. The speech signal is preprocessed to remove unnecessary inflection points due to the high frequency components using a low pass filter. Only the inflection points from local maxima are used to get the pitch period. While the existing pitch estimation methods process speech signals in blockwise, the proposed method detects the inflection points in sample and produces the pitch period/fundamental frequency estimates along the time. Computer simulation shows the usefulness of the proposed method as a fundamental frequency estimator.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.635-638
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• 2005

The curve shape of the time fluctuation extracted from the electromagnetic signals is very complex. Thus it is important to decide exactly the signal property such as the inflection point for the observed signal. Usually filters elaborately designed are used to detect the signal characteristics. When the noise is added to the signal, the inflection point can be detected using the observation filter. In this paper we propose the design method for a natural observation filter with optimal filter order to extract a definite inflection point for the case of signals with the mixed noise.

• KIEE International Transactions on Power Engineering
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• v.3A no.2
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• pp.85-92
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• 2003

When a current transformer (CT) is saturated, the wave-shape of the secondary current is distorted and contains points of inflection, which correspond to the start or end of each saturation period. Discontinuity in the first-difference function of the current arises at points of inflection, where the second and third differences convert into pulses that can be used to detect saturation. This paper describes the design and evaluation of a CT saturation detection technique using the third-difference function and includes the countermeasure for a spike signal. Test results clearly demonstrate that the algorithm successfully detects the start and end of each saturation period irrespective of the remanent flux and magnetization inductance in the saturated region. This paper concludes by describing the results of hardware implementation of the algorithm using a DSP.