X(z) of a system is specified by a pole-zero pattern as shown:
Consider three different solutions of x(n)
\({x_1}\left( n \right) = \left[ {{2^n} - {{\left( {\frac{1}{3}} \right)}^n}} \right]u\left( n \right)\)
\({x_2}\left( n \right) = - {2^n}u\left( {-n - 1} \right) - \frac{1}{{{3^n}}}u\left( n \right)\)
\({x_3}\left( n \right) = - {2^n}u\left( {-n - 1} \right) + \frac{1}{{{3^n}}}u\left( { - n - 1} \right)\)
Which of the above solution(s) is/are possible for X(z)
1
x1(n)
2
x2(n)
3
x3(n)
4
all the above