Read Lathi section 5.3. Do exercise E5.9, page 371.

*Solution.
*

Shift right by 2,

= | 5f[k-1]-f[k-2] |
(1) |

Using unilateral z-transform,

y[k] |
Y(z) |
(2) | |

y[k-1] |
(3) | ||

y[k-2] |
(4) | ||

f[k-1] |
(5) | ||

f[k-2] |
(6) |

z-transform of Eq.(1) is

= | (7) | ||

= | (8) | ||

= | (9) |

Now Y(z) is

Y(z) |
= | (10) |

Break Y(z) into partial fractions

= | (11) | ||

= | (12) |

= | (13) | ||

Y(z) |
= | (14) |

Taking inverse z-transform

y[k] |
= | (15) | |

= | (16) |