Interpolating FIR filters: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
Cdxskier (talk | contribs)
Created page with 'This page offers a brief explanation of interpolation FIR filters. ==Example== Assume we start with the sample <math> \ [1 2 3 4 3 2 1] </math>. Padding with zeros gives: …'
 
Cdxskier (talk | contribs)
No edit summary
Line 4: Line 4:
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>)
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>
 
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 14:10, 16 November 2010

This page offers a brief explanation of interpolation FIR filters.

Example

Assume we start with the sample [1234321]. Padding with zeros gives: [1020304030201]. Let's apply 2 filters.

Filter 1: [11] (also written as y(kT)=1.0*x(kT)+1.0*x(k1)T). This filter gives: [112233445544332211]. This is a hold function.

Filter 2: [0.510.5] (also written as y(kT)=0.5*x(kT)+1.0*x(k1)T+0.5*x(k2)T

This filter gives: [.51.01.52.02.53.03.54.04.55.04.54.03.53.02.52.01.51.00.5]. This is a linear interpolater.