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Relation between residue integration and the Dirac Delta function

  1. Nov 14, 2013 #1
    1. The problem statement, all variables and given/known data

    OK so I'm doing a course on Signals and Systems and I'm taking inverse z transforms using residue integration. One particular formula in complex integration made me think a bit.

    [itex]\oint{\frac{f(z)}{z-z_0} dz} = 2\pi jf(z_0)[/itex]

    This looks eerily similar to the definition for the unit impulse function:

    [itex]\int_{-∞}^{∞}{f(t)δ(t-t_0)} = f(t_0)[/itex]

    I was wondering if there was any relation between these two ideas. Is the unit impulse some sort of "Real projection" of the 1/z function?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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