Joseph Fourier first represented Fourier integral theorem in the following DOE: File:Http://d.hiphotos.baidu.com/album/s=1100;q=90/sign=8f613fd8e7cd7b89ed6c3e823f1479d6/faf2b2119313b07e91e66f1a0dd7912397dd8c4c.jpg[1] Which is then introduced into the first delta function as following: File:Http://e.hiphotos.baidu.com/album/s=1100;q=90/sign=87a0c9dffd039245a5b5e50eb7a49fb3/1b4c510fd9f9d72a24372f0fd52a2834349bbb54.jpg[1] And the end end up with what mathematicians called Dirac delta function: File:Http://d.hiphotos.baidu.com/album/s=1100;q=90/sign=efcf66a3810a19d8cf03800403cab9fa/622762d0f703918f839c02d8503d269759eec456.jpg [1] The input x(t) is a function with a fundamental period x(t)= 1 from x= 0 to 1 and f(x)= -1 to 0, with a discontinuity at x=0. The following graphs from matlab represents Gibbs phenomena, as n increases the overshot decreases. File:Http://e.hiphotos.baidu.com/album/s=1100;q=90/sign=2e3f690563d0f703e2b291dd38ca6a4c/18d8bc3eb13533fa26a7ac3ca9d3fd1f41345b8a.jpg File:Http://f.hiphotos.baidu.com/album/s=1100;q=90/sign=72fdab66ac345982c18ae1933cc40adc/d01373f082025aaf412f41d9faedab64034f1a86.jpg File:Http://g.hiphotos.baidu.com/album/s=1100;q=90/sign=4764a7165882b2b7a39f3dc5019df09e/72f082025aafa40faddbf1cfaa64034f78f01986.jpgFile:Http://f.hiphotos.baidu.com/album/s=1100;q=90/sign=632030d13b87e9504617f76d20086832/d1160924ab18972b01273fd8e7cd7b899e510a86.jpg Back to the 2nd bonus point opportunity, ECE301 Spring 2013
