Find
[1 0 0 1]
and plot the magnitude and phase of *F*_{r}. Find the
of *F*_{r} to verify it is equal to [1 0 0 1] as expected.

*Solution.
*

The DFT of *f*_{k} is

F_{r} |
= | (17) | |

= | (18) | ||

= | (19) |

The magnitude and phase responses are

|F_{r}| |
= | (20) | |

arg(F_{r}) |
= | (21) |

The IDFT of *F*_{r} is

f_{k} |
= | (22) | |

= | (23) |

Using

= | (24) |

where

*f*_{k} is

f_{k} |
= | (25) | |

= | (26) |

or