(a) Find y(n) for x(n) as above for the system y(n) = ay(n-1) + x(n-1)

(b) Draw a block diagram of this system.

*Solution.*

(a) In this case, the output is the sum of past outputs as well as the past inputs.

n | x(n) | x(n-1) | y(n) |

0 | 1 | 0 | 0 |

1 | 1 | 1 | 1 |

2 | 0 | 1 | a+1 |

3 | 0 | 0 | a*(a+1) |

4 | 0 | 0 | a*a*(a+1) |

. | . | . | ... |

(b) The block diagram of this system is as follows: