Interpolating FIR filters: Difference between revisions
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Filter 1: <math> \ [1 \ 1] </math> (also written as <math> \ y(kT)=1.0 |
Filter 1: <math> \ [1 \ 1] </math> (also written as <math> \ y(kT)=1.0 \cdot x(kT) + 1.0 \cdot x(k-1)T </math>). |
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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. |
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. |
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Filter 2: <math> \ [0.5 \ 1 \ 0.5] </math> (also written as <math> \ y(kT)=0.5 |
Filter 2: <math> \ [0.5 \ 1 \ 0.5] </math> (also written as <math> \ y(kT)=0.5 \cdot x(kT) + 1.0 \cdot x(k-1)T + 0.5 \cdot x(k-2)T </math> |
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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 14:48, 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.
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.