Question

solve the fibinacci recursion formula to a closed form usung the inverse z-transform

Z --U Fix is furtf 6 F-1 = f -z = 1 fica fkul + F 1 U = Z CU U 42

Answer 1

form using ! for mula to a closed solve Fibonacci recursion the inverse a-tromsform. . . So Fibonacci recurrence ...Fk+2 = Fkti tik.. Fo= 0 F1 = 1 Uk+2 = Ukti + UK Coro Wi= (0 ) .. Apply the Z.T . Z CUK+2 ) = ZC Ux+1) + z(uk) z(xn+k)) = zk( xiz) – 202-2011 2 ' _(272?_-(k)**) Z(X(n+x)) = 2KX125 – xc7zk - zrzki-(2zk-22(+)z

ZC Uk+2) = z2(UZ) - uro) - CU) ') = za ufz)- 02?12' = Z²uEl-Z ZC Uk +1) = Z CUZ) - 410)) = ZUZ) - 0. z cuk+i)= ZUZ) z cuk) - UZ) Z CUK+2) – zluk +1) - zluk) = 0 z’uz 2-- Zucz) – UIZ) = 0 (72-3-1) UZ) = Z.

ua) Z? 7-1 - +1 +1 +4 22 2. (1755). op 12-1995) 12–195) -12) (13 Da 03 zcantina za Apply Inversezat zlewmeyin) - Z Zurz I'C Z UK = uts de la Farms -- (fe_vf*un fax = a (5) * = (1-3 * 2 cm) Thea hace uyum (1976) un