<p>Bumping this thread for a quick question:</p>
<p>Do Fourier series or transforms have a place in Chem. E?</p>
<p>Maybe this will help: [Amazon.com:</a> Who Is Fourier?: A Mathematical Adventure: Transnational College of LEX: Books](<a href=“http://www.amazon.com/Who-Fourier-Mathematical-Transnational-College/dp/0964350408/ref=sr_1_1?ie=UTF8&s=books&qid=1238794649&sr=1-1]Amazon.com:”>http://www.amazon.com/Who-Fourier-Mathematical-Transnational-College/dp/0964350408/ref=sr_1_1?ie=UTF8&s=books&qid=1238794649&sr=1-1)
It’s a kind of cartoon version explaining the math, FFTs, etc. put together by an interesting Japanese language group.</p>
<p>Xav, three years after starting this thread, I have seen tons of fourier/laplace transforms in many fields. I don’t know, but I would bet that they have some applications in Chem E.</p>
<p>If the make Chem. Eng. majors take Quantum Physics or rigorous Electrodynamics, then yes, yes, yes.</p>
<p>There’s a site here with the transforms written in equation editor. Save’s a heck
of a lot of time having to type it. </p>
<p>[Peter</a> J. Vis - Signal Processing Mathematics](<a href=“http://www.petervis.co.cc/mathematics/sigprocess.html]Peter”>http://www.petervis.co.cc/mathematics/sigprocess.html)</p>
<p>hope it helps</p>
<p>I know it’s a bit late, but I’m curious if anyone else sees fourier transforms the same way as me. Basically, in real space you see repeating signals as something that cycles on forever. When you do a fourier transform, you’re instead looking at the space between “peaks,” and, as such, can see those infinitely repeated signals as single points.</p>
<p>In my case it’s useful when looking at a crystal. Atoms are spaced at very regular intervals, so in real space it can be difficult to measure precisely the distance between them. However, in fourier space the typical spacing is represented by a single point (in a perfect crystal with no vibrations) or by a blurred out shape depending on how imperfections influence the repeating structure.</p>
<p>I’ve seen FFT’s (Fast Fourier Transforms) used all of the time when dealing with measuring numerous types of frequencies. I personally have used them in a lab when analyzing the vortex shedding frequency of a cylinder in a wind tunnel.</p>
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<p>I’m not exactly sure what you mean. Are you talking about the fact that periodic signals have discrete Fourier components (that is, they are just some arrangement of spikes)?</p>
<p>I guess. It’s not just that they have peaks, but there’s a correlation between certain values at certain spatial (or time) distances. Like, for example, in seismology I imagine a time-domain picture of an earthquake is crazy confusing, yet if you take a fourier transform of it, you might have an easier time picking out individual processes which are occurring since your eyes don’t need to do the pattern recognition for repeating processes since it’s already been done for you.</p>
<p>I guess it’s hard for me to explain since I’m atrocious in math and never really learned FTs properly in math. I’ve only seen them as a tool to look at physical processes and a way to solve some integrals (though I never really attained any physical or intuitive understanding into this process).</p>