Message:

<p>[QUOTE=&quot;mrbrklyn, post: 926107, member: 4381&quot;]In mathematics, the Fourier transform (often abbreviated FT) is an operation that transforms one complex-valued function of a real variable into another. In such applications as signal processing, the domain of the original function is typically time and is accordingly called the time domain. The domain of the new function is typically called the frequency domain, and the new function itself is called the frequency domain representation of the original function. It describes which frequencies are present in the original function. This is analogous to describing a musical chord in terms of the notes being played. In effect, the Fourier transform decomposes a function into oscillatory functions. The term Fourier transform refers both to the frequency domain representation of a function, and to the process or formula that &quot;transforms&quot; one function into the other.</p><p>There are several common conventions for defining the Fourier transform of an <a href="http://en.wikipedia.org/wiki/Lebesgue_integration" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Lebesgue_integration" rel="nofollow">integrable</a> function <i>ƒ</i> : <b>R</b> → <b>C</b> (<a href="http://en.wikipedia.org/wiki/Fourier_transform#CITEREFKaiser1994" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Fourier_transform#CITEREFKaiser1994" rel="nofollow">Kaiser 1994</a>). This article will use the definition:</p><p>&nbsp;<img src="http://upload.wikimedia.org/math/f/c/7/fc74da34236f93b1cf1bbecd9394597c.png" class="bbCodeImage wysiwygImage" alt="" unselectable="on" />&nbsp;&nbsp; for every <a href="http://en.wikipedia.org/wiki/Real_number" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Real_number" rel="nofollow">real number</a> <a href="http://en.wikipedia.org/wiki/Xi_%28letter%29" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Xi_%28letter%29" rel="nofollow"><i>ξ</i></a>. When the independent variable <i>x</i> represents <i>time</i> (with <a href="http://en.wikipedia.org/wiki/SI" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/SI" rel="nofollow">SI</a> unit of <a href="http://en.wikipedia.org/wiki/Second" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Second" rel="nofollow">seconds</a>), the transform variable <i>ξ</i>&nbsp; represents <a href="http://en.wikipedia.org/wiki/Frequency" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Frequency" rel="nofollow">frequency</a> (in <a href="http://en.wikipedia.org/wiki/Hertz" target="_blank" class="externalLink ProxyLink" data-proxy-href="http://en.wikipedia.org/wiki/Hertz" rel="nofollow">hertz</a>). Under suitable conditions, <i>ƒ</i> can be reconstructed from <img src="http://upload.wikimedia.org/math/e/d/8/ed8db25ddc99da2e7e5a7e3e5c2e48cb.png" class="bbCodeImage wysiwygImage" alt="" unselectable="on" /> by the <b>inverse transform</b>:</p><p>&nbsp;<img src="http://upload.wikimedia.org/math/4/6/2/462af56cbf744659150d848728a03b49.png" class="bbCodeImage wysiwygImage" alt="" unselectable="on" />&nbsp;&nbsp; for every real number <i>x</i>.[/QUOTE]</p><p><br /></p>

Your name or email address:

Do you already have an account?

• No, create an account now.
• Yes, my password is:
• Forgot your password?

Stay logged in