The impulse response of a second-order Linear Time-Invariant digital filter characterized by
\(H\left( z \right) = \frac{{\left( {\alpha - \beta } \right){z^{ - 1}}}}{{\left( {1 - {\alpha ^{ - 1}}} \right)\left( {1 - \beta {z^{ - 1}}} \right)}}\left| \alpha \right| < 1 < \left| \beta \right|with\;ROC\;\left| \alpha \right| < \left| z \right| < \left| \beta \right|\) is given by:1
h(n) = αn u(n) – βn u (n)
2
h(n) = αn u(n) + βn u(-n – 1)
3
h(n) = =αn u(-n -1) + βn u (-n – 1)
4
h(n) = αn u(-n – 1) + βn u (- n-1)