Z-33 - Z­Tra nsform of sin/ c os Time Doma in u(k) = e...

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Unformatted text preview: Z­Tra nsform of sin/ c os Time Doma in u(k) = e ikθ u(k) = e ­ikθ Z­Tra nsform U(z) = U(z) = 1­ e ⋅ z­1 iθ 1 1­ e ⋅ z­1 ­iθ 1 u(k) = c os(kθ ) = e ikθ +e 2 − ikθ 1 1 U(z) = ( iθ ­1 + )/ 2 1­ e ⋅ z 1− e − iθ ⋅ z−1 1 1 =( + )/ 2 1− c osθ ⋅ z−1 − isin θ ⋅ z−1 1− c osθ ⋅ z−1 + isin θ ⋅ z−1 1− c osθ ⋅ z−1 = (1− c osθ ⋅ z−1)2 + (sin θ ⋅ z−1)2 = 1− c osθ ⋅ z−1 1− 2c osθ ⋅ z−1 + z− 2 u(k) = sin(kθ ) = e ikθ − e − ikθ 2i U(z) = sin θ ⋅ z­1 1­ 2c osθ ⋅ z­1 + z− 2 C S851: Feed b a c k Control for Comp uter Systems ...
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