Revision as of 10:33, 11 March 2013 by Wang676 (Talk | contribs)

1.Impulse response

Joseph Fourier first represented Fourier integral theorem in the following DOE:

DOE1.jpg[1]
Which is then introduced into the first delta function as following:

DOE2.jpg[1]
And the end end up with what mathematicians called Dirac delta function:

DOE3.jpg [1]
[1] “Dirac delta function. Internet: http://en.wikipedia.org/wiki/Dirac_delta_function, March. 8, 2013 [March. 10, 2013].

2.Fourier series

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.

N=25.jpg N=50.jpg N=100.jpg
3.Filters

The upper is the Gaussian filter, while bottom is the unsharp.

Figrelena.jpg
Back to the 2nd bonus point opportunity, ECE301 Spring 2013

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