Interpolating FIR filters
This page offers a brief explanation of interpolation FIR filters.
Assume we start with the sample . Padding with zeros gives: . Let's apply 2 filters.
Filter 1: (also written as ).
This filter gives: . This is a hold function.
Filter 2: (also written as
This filter gives: . This is a linear interpolater.
I had a lot of trouble finding generic information about the number of multiply/add operations used in an interpolation FIR filter. I did find formula for the number of multiply/add operation used by the MATLAB function upfirdn, which upsamples, applies an FIR filter, and then downsamples. It is: where and are the lengths of (the impulse response of the FIR filter) and (the original signal), respectively.
Check out my article on Decimating FIR filters.