• 전기학회논문지
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• 제64권4호
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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.

• 전기학회논문지
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• 제67권2호
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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.

• 전기학회논문지
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• 제61권11호
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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.

• 전자공학회논문지B
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• 제31B권5호
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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.

• 전기학회논문지
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• 제61권1호
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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.

• 한국산학기술학회논문지
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• 제21권1호
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• pp.753-759
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• 2020

본 논문에서는 통과대역에서 점진적으로 감소하는 리플을 갖는 변형된 체비세프 저역통과 필터 함수를 제안하고, 주파수 영역에서 특성을 분석하였다. 제안된 체비세프 함수는 점진적으로 감소하는 크기 특성에 의해 기존의 체비세프 함수보다 통과대역에서 크기 특성이 크게 개선되었다. 이러한 크기 특성의 변화로 위상 특성도 선형적인 특성을 갖고. 시간지연은 최고점과 최저점의 차이가 현저히 감소되면서 시간지연 특성이 개선되었다. 또한, 제안된 체비세프 함수는 짝수와 홀수 차수를 포함하는 모든 차수에서 최대전력전송이 가능한 수동 복종단 제자형 회로망으로 실현이 가능하고, 모의법을 이용하면 낮은 감도 특성을 갖는 능동 RC 필터 또는 스위치드 커패시터 필터로도 구현할 수 있다. 제안된 체비세프 필터의 특성을 고찰하기 위하여 6차 수동 복종단 제자형 저역통과 필터를 설계하였고, MATLAB과 SPICE 프로그램으로 필터 특성을 분석하였다. 제안된 체비세프 함수는 기존의 체비세프 함수가 갖는 문제점을 해결할 수 있으며, 각종 신호처리용 필터 설계에 사용 시 필터 크기, 위상, 시간 지연 특성 개선에 활용할 수 있다.

• 한국전자파학회논문지
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• 제8권6호
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• pp.620-628
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• 1997

Chebyshev 함수에 의하여 테이퍼형 선로를 설계할 때 Chebyshev 함수는 테이퍼 길이가 한 파장근처에서 임 피던스 불연속을 발생시켜 실제 제작된 선로는 그 특성이 나빠진다. 이를 보완하기 위하여 이 함수들을 중첩시켜 불연속이 제거된 새로운 함수를 이 논문에서 제안하였다. 이 개선된 함수를 이용하여 구형과 원형 도파관과의 트랜지션을 설계하였으며 기존 방법으로 설계하였을 때보 다 반사손실이 5dB 이상 개선되었음을 보여주었다.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2017년도 추계학술대회
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• pp.256-257
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• 2017

실내환경에서는 GPS 신호를 사용할 수 없으므로 드론의 고도 측정에 주로 대기압 센서가 사용된다. 본 논문에서는 대기압 센서 측정값의 고주파 오차를 줄이기 위해 Chebyshev 필터를 사용하는 방법을 제안한다. 드론 제어기의 성능을 고려하여 필터의 차수는 3차로 제한하며 Chebyshev 필터의 전달함수를 구한다.

• Kyungpook Mathematical Journal
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• 제58권1호
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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.

• 대한수학회보
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• 제45권3호
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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.