https://fweb.wallawalla.edu/class-wiki/index.php?title=Daniel_Liwag&feed=atom&action=historyDaniel Liwag - Revision history2024-03-29T08:33:43ZRevision history for this page on the wikiMediaWiki 1.39.1https://fweb.wallawalla.edu/class-wiki/index.php?title=Daniel_Liwag&diff=10927&oldid=prevBrian.Clark at 21:37, 18 December 20132013-12-18T21:37:57Z<p></p>
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</table>Brian.Clarkhttps://fweb.wallawalla.edu/class-wiki/index.php?title=Daniel_Liwag&diff=10926&oldid=prevBrian.Clark at 21:37, 18 December 20132013-12-18T21:37:19Z<p></p>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td>
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</table>Brian.Clarkhttps://fweb.wallawalla.edu/class-wiki/index.php?title=Daniel_Liwag&diff=10923&oldid=prevDaniel.liwag at 21:04, 18 December 20132013-12-18T21:04:17Z<p></p>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If we choose a factor D <= M with three factors, D<sub>1</sub>, D<sub>2</sub>, and D<sub>3</sub> such that D = D<sub>1</sub> * D<sub>2</sub> * D<sub>3</sub> , we can have a 3-stage filter design, with one filter for each stage. The specifications for each stage filter depend on the original narrow lowpass filter and the stage factors D<sub>1</sub>, D<sub>2</sub>, and D<sub>3</sub>.</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If we choose a factor D <= M with three factors, D<sub>1</sub>, D<sub>2</sub>, and D<sub>3</sub> such that D = D<sub>1</sub> * D<sub>2</sub> * D<sub>3</sub> , we can have a 3-stage filter design, with one filter for each stage. The specifications for each stage filter depend on the original narrow lowpass filter and the stage factors D<sub>1</sub>, D<sub>2</sub>, and D<sub>3</sub>.</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The choice of decimator D and number of stages and factors for each stage is not a single-objective optimization problem. This system will give a set of 'best decimators' for the user to select.</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The choice of decimator D and number of stages and factors for each stage is not a single-objective optimization problem. This system will give a set of 'best decimators' for the user to select.</div></td>
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</table>Daniel.liwaghttps://fweb.wallawalla.edu/class-wiki/index.php?title=Daniel_Liwag&diff=10920&oldid=prevDaniel.liwag: Created page with "'''Multi-Stage FIlter Design''' Consider a narrow lowpass filter. Let <math>M = (sample rate * 0.5)/(stopband frequency)</math> where M is the maximum decimator for the narrow …"2013-12-18T19:44:28Z<p>Created page with "'''Multi-Stage FIlter Design''' Consider a narrow lowpass filter. Let <math>M = (sample rate * 0.5)/(stopband frequency)</math> where M is the maximum decimator for the narrow …"</p>
<p><b>New page</b></p><div>'''Multi-Stage FIlter Design'''<br />
<br />
<br />
Consider a narrow lowpass filter. Let <math>M = (sample rate * 0.5)/(stopband frequency)</math> where M is the maximum decimator for the narrow lowpass filter (any integer greater than M used as a decimator will cause signal aliasing in the passband region).<br />
<br />
If we choose a factor D <= M with three factors, D<sub>1</sub>, D<sub>2</sub>, and D<sub>3</sub> such that D = D<sub>1</sub> * D<sub>2</sub> * D<sub>3</sub> , we can have a 3-stage filter design, with one filter for each stage. The specifications for each stage filter depend on the original narrow lowpass filter and the stage factors D<sub>1</sub>, D<sub>2</sub>, and D<sub>3</sub>.<br />
<br />
Let L<sub>1</sub>, L<sub>2</sub>, and L<sub>3</sub> be the filter lengths for each stage respectively, then the total computations per D samples can be formulated as 2*(L<sub>3</sub> + L<sub>2</sub> * D<sub>3</sub> + L<sub>1</sub> * D<sub>3</sub> * D<sub>2</sub>) and the group delay is N = (L<sub>1</sub> - 1) + D<sub>1</sub> * (L<sub>2</sub> - 1) + D<sub>1</sub> * D<sub>2</sub> * (L<sub>3</sub> - 1)<br />
<br />
However, if the last stage factor is D<sub>3</sub> = 2, and since there is no gain in computational efficiency for the model 2, then model 1 is used for this stage. In this case, the group delay is N = (L<sub>1</sub> - 1) + D<sub>1</sub> * (L<sub>2</sub> - 1) + D<sub>1</sub> * D<sub>2</sub> * (L<sub>3</sub> - 1)/2<br />
<br />
For most optimal designs, the last stage factor is 2. If L<sub>3</sub> is an odd number, N is always an integer. If there is half a sample delay (N is not an integer), problems will occur for wide lowpass and highpass filters where an integer group delay is required. This system will adjust the filter length in order to avoid the half-sample delay in these two filters.<br />
<br />
The choice of decimator D and number of stages and factors for each stage is not a single-objective optimization problem. This system will give a set of 'best decimators' for the user to select.<br />
<br />
<br />
== References ==<br />
[https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CC4QFjAA&url=http%3A%2F%2Fwww.mds.com%2Fsystem%2Fresources%2FBAhbBlsHOgZmIjIyMDExLzA1LzAzLzEyLzI0LzM5LzQ4Ny9tdWx0aXJhdGVfYXJ0aWNsZS5wZGY%2Fmultirate_article.pdf&ei=zSalUoGrK4nsoATOl4DQCQ&usg=AFQjCNGTQ9MYLLQE6D4ay_pDlGzShSA1uw&sig2=geMUjuDMkKvs79FrwJeeQg&bvm=bv.57752919,d.cGU Multirate Filter Design - An Introduction, by Jerry Purcell, Ph.D.]<br />
<references /></div>Daniel.liwag