Ideal D/A Conversion

Each sample in the time domain scales and locates one sinc function in the unique, continuous, bandlimited interpolation of the sampled signal.

Convolving a sampled signal $y(n)$ with sinc$(n-\eta)$ ``evaluates'' the signal at an arbitrary continuous time $\eta\in\mathbb{R}$ :

$$\begin{eqnarray*} y(\eta) &=& \sum_{n=-\infty}^\infty y(n) \mbox{sinc}(\eta-n)\\ [10pt] \end{eqnarray*}$$

Proof: Sampling Theorem