Question

求下列函数的Z反变换X(z)=1/(z+1)(z+2)

Answer 1

1/(z+1)(z+2)=1/(z+1)-1/(z+2)

z/(z+1)(z+2)=z/(z+1)-z/(z+2)

(1)if the region is |z|>2

both terms are causal

the signal is (-(-1)^n+2(-2)^n)*u(n+1)

(2)if the region is 2>|z|>1

the first is causal and the second is anticausal

the signal is -(-1)^nu(n+1)-2*(-2)^n*u(-n-2)

(3)if the region is |z|