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On the operational matrices of block pulse functions
Authors:CHYI HWANG  YEN-PING SHIH
Affiliation:1. Department of Chemical Engineering , National Cheng Kung University , Tainan, Taiwan, 700, Republic of China;2. Department of Chemical Engineering and Technology , National Taiwan Institute of Technology , Taipei, Taiwan, 107, Republic of China
Abstract:It is pointed out that the mathematical bases for block pulse operational methods to various dynamic system problems are to represent the delay operator exp(— hs)approximately by  /></span> and to represent exp ( — α<i>hs</i>) approximately by (1 — α) + α exp ( — <i>hs</i>), where 0 ≤ α ≤ 1. On these bases, all the existing block pulse operational matrices—the integration matrix, the convolution matrix, the correlation matrix, the delay matrix, and the stretch matrix—can be derived in a mathematically rigorous way without having to use graphical demonstrations.</td>
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