Linear Interpolation (Implementation)

The fractional part of the delay, $\delta$, effectively determines how far to go along the line between samples.

A fractional delay $\hat{x}(n-(M + \delta))$, reads from the delay line at neighbouring delays $M$ and $M+1$, and takes the weighted sum of the outputs:

$$\hat{x}(n - (M+\delta)) = (1-\delta)x(n-M) +\delta x(n-(M+1)),$$

where $M$ is the integer and $\delta$ is the fractional part.

Notice that if $\delta=0$, the fractional delay reduces to the regular integer delay.

Linear interpolation in a circular delay line (Matlab):

if (outPtr==1)
  z = (1-delta)*dline(outPtr) + delta*dline(Mmax);
else
  z = (1-delta)*dline(outPtr) + delta*dline(outPtr-1);
end