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:

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