# Relation between residue integration and the Dirac Delta function

1. Nov 14, 2013

### ashwinnarayan

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.

$\oint{\frac{f(z)}{z-z_0} dz} = 2\pi jf(z_0)$

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

$\int_{-∞}^{∞}{f(t)δ(t-t_0)} = f(t_0)$

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