https://fweb.wallawalla.edu/class-wiki/index.php?action=history&feed=atom&title=4_-_Fourier_Transform 2026-05-18T06:47:33Z Revision history for this page on the wiki MediaWiki 1.43.0 https://fweb.wallawalla.edu/class-wiki/index.php?title=4_-_Fourier_Transform&diff=5686&oldid=prev 2009-11-08T04:42:26Z

<p>New page: <a href="/class-wiki/index.php/Kevin_Starkey" title="Kevin Starkey">Kevin Starkey</a> &lt;br&gt; Find &lt;math&gt; \mathcal{F}\left[\int_{-\infty}^ \infty s(t)dt\right]&lt;/math&gt; &lt;br&gt; First we know that &lt;math&gt; \mathcal{F}\left[\int_{-\infty}^ \infty s(t)dt\right] = \int_...</p> <p><b>New page</b></p><div>[[Kevin Starkey]] &lt;br&gt;<br /> Find &lt;math&gt; \mathcal{F}\left[\int_{-\infty}^ \infty s(t)dt\right]&lt;/math&gt; &lt;br&gt;<br /> First we know that &lt;math&gt; \mathcal{F}\left[\int_{-\infty}^ \infty s(t)dt\right] = \int_{-\infty}^\infty\left(\int_{-\infty}^ \infty s(t)dt\right)e^{j2\pi ft} dt &lt;/math&gt; &lt;br&gt;<br /> We also know that &lt;math&gt; \mathcal{F}\left[s(t)\right] = S(f) and \int_{-\infty}^ \infty e^{j2\pi ft} dt = \delta(f) &lt;/math&gt; &lt;br&gt;<br /> Which gives us &lt;math&gt; \int_{-\infty}^\infty\left(\int_{-\infty}^ \infty s(t)dt\right)e^{j2\pi ft} dt = \int_{-\infty}^ \infty S(f) \delta (f)df &lt;/math&gt; &lt;br&gt;<br /> Since &lt;math&gt; \int_{-\infty}^ \infty \delta (f) df &lt;/math&gt; is only non-zero at f = 0 this yeilds &lt;br&gt;<br /> &lt;math&gt; \int_{-\infty}^ \infty S(f) \delta (f)df = S(0) &lt;/math&gt; &lt;br&gt;<br /> So &lt;math&gt; \mathcal{F}\left[\int_{-\infty}^ \infty s(t)dt\right] = S(0)</div>

Kevin.Starkey