# Interpolating FIR filters

This page offers a brief explanation of interpolation FIR filters.

## Example

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.

## Multiply/add Operations

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.

## Related Topics

Check out my article on Decimating FIR filters.