ELEC 310 Midterm: ELEC 310 UVic Elec 310 Midterm 2 Mar 2 2004
31 Jan 2019
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/40: this is a closed book examination, a formula sheet is provided, non-programmable calculators are allowed. The z transform of f(nt ) is de ned as. F(z) = z {f(nt )} = f(kt )z k. Clearly, the right hand side of the above equation is a. We can therefore nd the inverse z trans- form by nding the co-e cients of a laurent series of. For causal functions, f(nt ) = 0 for all n < 0, we are interested in the laurent series in the outer annuli |z| > |pm| where pm is the pole of f(z) farthest from the origin. F(nt ) + g(nt ) f(nt mt ) w n f(nt ) nt f(nt ) 0 n 6= 0 u(nt ) = 1 n 0. 0 n < 0 r(nt ) = nt n 0 n < 0. Kwn u(nt ) e nt u(nt ) sin( nt ) u(nt ) cos( nt ) u(nt )
