| 采用移位切比雪夫多项式求解卷积的新方法 |
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| 引用本文： | 范一平,俞金寿,蒋慰孙.采用移位切比雪夫多项式求解卷积的新方法[J].医学教育探索,1988(2). |
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| 作者姓名： | 范一平 俞金寿 蒋慰孙 |
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| 作者单位： | 华东化工学院自动化研究所
(范一平，俞金寿)，华东化工学院自动化研究所(蒋慰孙) |
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| 摘 要： | 本文首次定义和推导了移位切比雪夫多项式(第一类和第二类)的分离矩阵,它具有简洁的递推关系和三角形结构。应用分离矩阵的性质,得到了一类求解卷积的新方法。数字仿真肯定了此方法的应用价值。分离矩阵还可以推广到脉冲响应函数的辨识、最优伺服机构的设计等控制领域。
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| 关 键 词： | 卷积 正交函数 切比雪夫逼近 解 |
New approach to the solution of convolution integral via shifted Chebyshev polynomials |
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| Fan Yiping,Yu Jinshou Jiang Weisun.New approach to the solution of convolution integral via shifted Chebyshev polynomials[J].Researches in Medical Education,1988(2). |
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| Authors: | Fan Yiping Yu Jinshou Jiang Weisun |
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| Institution: | Research institute of automatic control |
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| Abstract: | The separative matrices of shifted Chebyshev polynomials of the first and second kinds, which have a nice structure and an elegant recursive formula, are introduced at the first time. By using the property of the separative matrices, a new approach to the convolution integral is presented. Two examples are included to demonstrate the validity and applicability of the approach. In addition, the separative matrices can be applied to the identification of impulse response of linear systems and the optimal design of linear servomachanisms. |
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| Keywords: | convolution orthogonal function chebyshev approximation solution |
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