The output of an analog derivator

can be approximated by:

y(t) = x'(t) |
x(t) - x(t-T) |

T | |

y(n) = x'(n) |
x(n) - x(t-1) |
= (1/T) x(n) - (1/T) x(n-1) = h(k) x(n-k) |

T | ||

and hence the impulse response of this simple digital derivator is

=> | h(0) = 1/T |

h(1) = -1/T | |

h(n) = 0 elsewhere | |

This is an FIR system.

Transfer function:

*H*(*z*) = *h*(*n*) *z ^{-n}* =

=> H(z) = |
1 | (1 - z)^{-1} |

T | ||

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