https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=130.126.255.92formulasearchengine - User contributions [en]2026-08-01T16:59:14ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Fundamental_matrix&diff=16631Fundamental matrix2013-10-15T01:21:11Z<p>130.126.255.92: /* Fundamental Matrix in Linear Systems */</p>
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<div>{{Orphan|date=September 2008}}<br />
A '''Fraser Filter''' is typically used in [[geophysics]] when displaying [[Very Low Frequency|VLF]] data. It is effectively the [[first derivative]] of the data.<br />
<br />
If <math>f(i) = f_i</math> represents the collected data then <math>average_{12}=\frac{f_1 + f_2}{2}</math> is the average of two values. Consider this value to be plotted between point 1 and point 2 and do the same with points 3 and 4: <math>average_{34}=\frac{f_3 + f_4}{2}</math><br />
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If <math>\Delta x</math> represents the space between each station along the line then<br />
<math>\frac{average_{12}-average_{34}}{2 \Delta x}=\frac{(f_1 + f_2)-(f_3 + f_4)}{4 \Delta x}</math> is the Fraser Filter of those four values.<br />
<br />
Since <math>4 \Delta x</math> is constant, it can be ignored and the Fraser Filter considered to be<br />
<math>(f_1 + f_2)-(f_3 + f_4)</math>.<br />
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==References==<br />
{{cite book |title=Applied Geophyisics |last=Telford |first=W.M.|coauthors=L.P. Geldart, R.E. Sheriff |pages=p480+ |edition=2nd}}<br />
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{{Geophysics-stub}}<br />
{{Signal-processing-stub}}<br />
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[[Category:Geophysics]]<br />
[[Category:Linear filters]]</div>130.126.255.92