• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.4
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• pp.598-604
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• 2015

A Chebyshev filter is well known for having a sharp skirt characteristic and equi-ripple. On the other hand, a Butterworth filter has a smooth skirt characteristic and maximally flat ripple. This paper analyzes the skirt characteristics of the filters with the cascade connection. The paper deals with the Chebyshev BPF, Cascading Chebyshev BPF, Butterworth BPF, Cascading Butterworth*Chebyshev BPF. First of all, the paper designs the prototype analog LPF in order to analyze skirt characteristics of the BPFs. Then the paper does the frequency transformation into the BPFs and tests the BPFs with cascading them. As a result, the skirt characteristics of the Chebyshev BPF was the sharpest and those of the Cascading Chebyshev BPF, Butterworth BPF, Cascading Butterworth*Chebyshev BPF was superior in order. The validity of the paper was confirmed through minute measurements of test results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.2
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• pp.255-260
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• 2018

This study is focusing on the trade-offs between the passband ripples and transition bands of the Chebyshev BPF, which is converted by using the Chebyshev LPF that is well known as a proto-type analog filter. It is also focusing on the trade-offs between the passband ripples and transition bands of the cascading Chebyshev BPF, as well as, the trade-offs between the two BPFs. The study finds the frequency responses of the proto-type analog LPF, the Chebyshev BPF and the cascading Chebyshev BPF. The study shows the results as comparative analysis tables. The study designs the 10th Chebyshev BPF in order to analyze it easily. The simulation results show that the Chebyshev BPF decreases about 55% of the transition band for the -2.5[dB] passband ripple comparing to the -0.5[dB] passband ripple. This study shows the effectiveness and economic feasibility in the restricted frequency communication environment for the decrease of the transition band as providing the passband ripple margin.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.11
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• pp.1700-1705
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• 2012

This study is focusing on ripple elimination in the band pass filter. There are generally two design methods in IIR filter design, which are a direct method and an indirect one. The indirect design method that designs the digital IIR LPF using the prototype analog LPF is applied to this study. A Butterworth filter and a Chebyshev filter are the typical prototype analog LPFs. This study shows characteristics of the digital IIR LPFs that are transformed from the prototype analog LPFs. The designed Butterworth and Chebyshev IIR LPFs are also designed as the band pass filters by frequency transformation in order to compare with the proposed cascading Chebyshev BPFs. This study shows frequency characteristics between the transformed IIR BPFs and the proposed cascading Chebyshev BPFs as well. The proposed cascading Chebyshev BPF is designed by cascading the different orders of Chebyshev BPFs. The aspect of the cascading filter is offsetting the ripples to descend them while the pass band ripples of the Chebyshev filter are ascending and vice versa. The designed cascading Chebyshev filter shows the flatness and the sharpness, which represent the advantages of Butterworth filter in the pass band and of Chebyshev filter in the transition band respectively. This result verifies the validity of the designed filter.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.88-94
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• 1994

Inverse Chebyshev function can realize the same order of Chebyshev function nuder the same specification. In general, inverse Chebyshev function has the preferable characteristics in terms of the delay characteristics and the time-domain performances compare with Chebyshev function. However, for the even order n, inverse Chebyshev function does not realize in the doubly-terminated ladder network which has preferable sensitivity characteristics because of the finite value at ${\omega}={\infty}$. In this paper, the modified inverse Chebyshev function with $\mid$H($j^{\infty}$$\mid$=0 s proposed to realize the passive doubly-terminated ladder network for the n even or odd. The modified inverse Chebyshev function characteristics ars studied in the frequency and time domain, and then, realize the passive doubly-terminated ladder network.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.168-172
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• 2012

This paper is focusing on the comparison of different kinds of BPFs(Band Pass Filters) passing signals with a particular frequency band. According to the different classifications, features and target application systems, BPF has many types. Chebyshev filter which has a steep slope and a few ripples, and Butterworth filter which has no ripple but gentle slope are the most typical BPFs. The ideal filter is flat in the passband and the slope in the transition band is perpendicular. In this paper, we suggest the cascading Chebyshev BPF with the advantages of the Chebyshev filter and the Butterworth filter simultaneously to make a closest filter to an ideal filter. The proposing BPF is the tenth Chebyshev BPF cascading the fourth and the sixth, and it is designed as the tenth cascading Chebyshev BPF. To measure the performance of the designing filter, we have compared and analyzed the tenth Chebyshev filter with the tenth Butterworth filter. As a result, the tenth cascading Chebyshev BPF has decreased the ripple more than 1/4 [dB] in the passband. Finally, the output of the simulation showed the validity of the proposing cascading Chebyshev filter.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.1
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• pp.753-759
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• 2020

A modified Chebyshev lowpass filter function with progressively diminishing ripples in the passband is proposed and analyzed in the frequency domain. Owing to the diminishing ripples, the passband magnitude characteristic of the proposed Chebyshev function has improved compared to the classical Chebyshev function. In addition, the phase characteristics of the proposed Chebyshev function were improved considerably compared to that of the Chebyshev function, and the time delay of the proposed function was much simpler and flatter. In addition, the proposed Chebyshev filter was realizable by the passive doubly terminated ladder network delivering maximum power transfer for the order n, even or odd, thus making themselves amenable to low-sensitivity active RC or switched capacitor filters through the simulation techniques. To verify the proposed Chebyshev filter characteristics, a 6th order passive doubly terminated ladder lowpass filter was designed and analyzed using the MATLAB and SPICE program. Thus, the proposed Chebyshev function can remove the drawbacks of the classical Chebyshev function and could be applicable to the design of a filter with an improved filter size, phase, and time delay characteristics for various signal processing.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.8 no.6
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• pp.620-628
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• 1997

When the Chebyshev function is applied to design the waveguide transition, it exhibits poor impedance matching characteristics due to impedance discontinuities at the ends of tapered line. In this paper, an improved Chebyshev function, which is obtained by using the convolution property, is proposed to make improvements on the impedance matching characteristics of the waveguide transition. When rectangular to circular waveguide transition is designed by improved function, then the computed return loss is approximately 5 dB better than the conventional Chebyshev function.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.256-257
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• 2017

Pressure sensors are usually used in the measurement of drone altitude in an indoor environment since GPS (global positioning system) signal is not available. In this paper, we propose a new method which uses the Chebyshev filter to decrease a high frequency error in the measured values of the pressure sensor. Considering performance of a drone flight controller, the filter order is limited to the $3^{rd}$ order. We explain the transfer function of the $3^{rd}$ order Chebyshev filter.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.55-66
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• 2018

By making use of the Riemann-Liouville fractional integrals, we establish further results on Chebyshev inequality. Other Steffensen integral results of the weighted Chebyshev functional are also proved. Some classical results of the paper:[ Steffensen's generalization of Chebyshev inequality. J. Math. Inequal., 9(1), (2015).] can be deduced as some special cases.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.601-606
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• 2008

The purpose of this paper is to introduce and discuss the concept of ${\omega}$-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that ${\omega}$-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.