Interpolation (linear)

Rather than rounding or truncating index values, it is more accurate to interpolate $x(n)$.

Linear interpolation of $x(y(n))$:

• consider a line between neighboring values of $x(n)$ indexed at the floor and ceiling of $y(n)$:

• a value that would lie on the line is inferred depending on the fractional part of the index.

Example: if $y(n)=6.5$, the inferred value would be on the line between $x(6)$ and $x(7)$, equidistant from indeces 6 and 7:

$$z(6.5) = \frac{x(6) + x(7)}{2} = .5x(6) + .5x(7)$$

More generally, for $y(n) = n.\eta$, where $n$ is the integer part and $\eta$ is the fractional part,

$$z(n+\eta) = (1-\eta)x(n) + (\eta)x(n+1),$$