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) |

where

A |
= | 2 | (15) |

B |
= | (16) | |

C |
= | (17) |

Now

F[z] |
= | (18) |

So applying the z-transform pair

(19) |

We take the inverse z-transform to obtain *f*[*n*]

f[n] |
= | Au[n] + B(3+j4)^{n}u[n] + C(3-j4)^{n}u[n] |
(20) |

= | (21) |

2.2

The numerical values for the first two terms are