Interpolating FIR filters
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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.
![{\displaystyle \ [1234321]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d660b25e5af1e8bb8ac47d8b7aa24adb5d32c5a2)
![{\displaystyle \ [1020304030201]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9dcbd2034514633c66cb6ff999858634ca9591f2)
Filter 1: (also written as ). This filter gives: . This is a hold function.
![{\displaystyle \ [11]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3cfaee18b0e0c268f0b647ec7244d41d6fc7c1bc)
![{\displaystyle \ [112233445544332211]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2af8f463556a73a52d262afabfee74209b8a14fc)
Filter 2: (also written as
![{\displaystyle \ [0.510.5]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c55599b33619bd79495a63ffd6130995b7de2fd5)
This filter gives: . This is a linear interpolater.
![{\displaystyle \ [.51.01.52.02.53.03.54.04.55.04.54.03.53.02.52.01.51.00.5]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/161df6f01976bca8fb6f44f8b523afd2440270ba)