2.1 Find the (causal) inverse z-transform of
F[z] | = | (12) |
using partial fractions.
2.2 Write numerical values for the coefficients of the first two tersm.
Solution.
2.1
The Eq.(13) can be expressed as a factored form
F[z] | = | (13) |
First break F(z) into partial fractions
= | (14) |
A | = | 2 | (15) |
B | = | (16) | |
C | = | (17) |
F[z] | = | (18) |
(19) |
We take the inverse z-transform to obtain f[n]
f[n] | = | Au[n] + B(3+j4)nu[n] + C(3-j4)nu[n] | (20) |
= | (21) |
2.2
The numerical values for the first two terms are