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Linear Interpolation

Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line.

More specifically, let $ \eta$ be a number between 0 and 1 which represents how far we want to interpolate a signal $ y$ between time $ n$ and time $ n+1$ . Then we can define the linearly interpolated value $ \hat y(n+\eta)$ as follows:

$\displaystyle \hat y(n+\eta) = (1-\eta) \cdot y(n) + \eta \cdot y(n+1) \protect$ (5.1)

For $ \eta=0$ , we get exactly $ \hat y(n)=y(n)$ , and for $ \eta=1$ , we get exactly $ \hat y(n+1)=y(n+1)$ . In between, the interpolation error $ \left\vert\hat y(n+\eta)-y(n+\eta)\right\vert$ is nonzero, except when $ y(t)$ happens to be a linear function between $ y(n)$ and $ y(n+1)$ .



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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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