Interpolating FIR filters: Difference between revisions

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==Example==
==Example==
Assume we start with the sample <math> \ [1 2 3 4 3 2 1] </math>. Padding with zeros gives: <math> \ [1 0 2 0 3 0 4 0 3 0 2 0 1] </math>. Let's apply 2 filters.
Assume we start with the sample <math> \ [1 \ 2 \ 3 \ 4 \ 3 \ 2 \ 1] </math>. Padding with zeros gives: <math> \ [1 \ 0 \ 2 \ 0 \ 3 \ 0 \ 4 \ 0 \ 3 \ 0 \ 2 \ 0 \ 1] </math>. Let's apply 2 filters.


Filter 1: <math> \ [1 1] </math> (also written as <math> \ y(kT)=1.0*x(kT) + 1.0*x(k-1)T </math>). This filter gives: <math> \ [1 1 2 2 3 3 4 4 5 5 4 4 3 3 2 2 1 1] </math>. This is a hold function.
Filter 1: <math> \ [1 \ 1] </math> (also written as <math> \ y(kT)=1.0*x(kT) + 1.0*x(k-1)T </math>). This filter gives: <math> \ [1 \ 1 \ 2 \ 2 \ 3 \ 3 \ 4 \ 4 \ 5 \ 5 \ 4 \ 4 \ 3 \ 3 \ 2 \ 2 \ 1 \ 1] </math>. This is a hold function.


Filter 2: <math> \ [0.5 1 0.5] </math> (also written as <math> \ y(kT)=0.5*x(kT) + 1.0*x(k-1)T + 0.5*x(k-2)T </math>
Filter 2: <math> \ [0.5 \ 1 \ 0.5] </math> (also written as <math> \ y(kT)=0.5*x(kT) + 1.0*x(k-1)T + 0.5*x(k-2)T </math>


This filter gives: <math> \ [.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5] </math>. This is a linear interpolater.
This filter gives: <math> \ [.5 \ 1.0 \ 1.5 \ 2.0 \ 2.5 \ 3.0 \ 3.5 \ 4.0 \ 4.5 \ 5.0 \ 4.5 \ 4.0 \ 3.5 \ 3.0 \ 2.5 \ 2.0 \ 1.5 \ 1.0 \ 0.5] </math>. This is a linear interpolater.

Revision as of 14:16, 16 November 2010

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.