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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{\bf R}$ :

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

Proof: Sampling Theorem


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``Bandlimited Interpolation, Fractional Delay Filtering, and Optimal FIR Filter Design'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-03-30 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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