Interpolating FIR filters: Difference between revisions
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==Multiply/add Operations== |
==Multiply/add Operations== |
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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: <math> \ (L_h L_x-pL_x)/q </math> where <math> \ L_h </math> and <math> \ L_x </math> are the lengths of <math> \ h[n] </math>(the impulse response of the FIR filter) and <math> \ x[n] </math>(the original signal), respectively. |
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: <math> \ (L_h L_x-pL_x)/q </math> where <math> \ L_h </math> and <math> \ L_x </math> are the lengths of <math> \ h[n] </math>(the impulse response of the FIR filter) and <math> \ x[n] </math>(the original signal), respectively. |
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==Related Topics== |
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Check out my article on [[Decimating FIR Filters]]. |
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===Author=== |
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[[Christopher Garrison Lau I]] |
Revision as of 17:26, 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.
Related Topics
Check out my article on Decimating FIR Filters.