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5 - Lecture 5 Open-Loop Systems Relation between E(s and...

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1 Lecture 5: Open-Loop Systems Relation between E * ( s ) and E ( z ) Pulse Transfer Function Open-Loop Systems with Digital Filters Reading: Chapter 4 of the textbook Relation Between E ( z ) and E * ( s ) e ( t ) e ¤ ( t ) e ( kT ) E ( z ) E ( s ) E ¤ ( s ) z = e Ts Sampler Data hold e ( t ) e ( kT ) ¹ e ( t ) sampler and hold Data hold e ( t ) e ¤ ( t ) ¹ e ( t ) T T Ideal sampler E ( z ) = P 1 k =0 e ( kT ) z ¡ k E ( z ) = P [ residues of E ( ¸ ) 1 1 ¡ z ¡ 1 e ] E ¤ ( s ) = P [ residues of E ( ¸ ) 1 1 ¡ e ¡ T ( s ¡ ¸ ) ] E ¤ ( s ) = 1 T P 1 k = ¡1 E ( s + jk! s ) + e (0) 2
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