The Spectrum of the Unit Impulse

Learn to derive the DFT of a unit impulse and observe the fundamental result.

Understanding the DFT starts with the spectrum of a unit impulse. This case gives us an interesting result, as we will now see.

The signal

A unit impulse is a signal that is 00 everywhere, except at time index 00 where its value is 11. In mathematical terms, we say:

δ[n]={1,n=00,n0\begin{equation*} \delta[n] = \left\{ \begin{array}{l} 1, \quad n = 0 \\ 0, \quad n \neq 0 \\ \end{array} \right. \end{equation*}

This is drawn in the figure below:

Get hands-on with 1200+ tech skills courses.