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--[[User:Mlo|Mlo]] 12:03, 13 January 2009 (UTC) | --[[User:Mlo|Mlo]] 12:03, 13 January 2009 (UTC) | ||
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| + | LaTex editor: http://thornahawk.unitedti.org/equationeditor/equationeditor.php | ||
Experimenting with inserting formulas to participate in hw discussion | Experimenting with inserting formulas to participate in hw discussion | ||
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Hw1: | Hw1: | ||
| − | <math>x_(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2})</math> | + | <math>x_(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2}) \quad (1)</math> |
Using the convolution property | Using the convolution property | ||
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where | where | ||
| − | <math>\mathcal{F} (cos(\frac{\pi t}{2})) = \frac{1}{2} [\delta(f - \frac{1}{4}) + \delta(f + \frac{1}{4})]</math> | + | <math>\mathcal{F} (cos(\frac{\pi t}{2})) = \frac{1}{2} [\delta(f - \frac{1}{4}) + \delta(f + \frac{1}{4})] </math> |
and | and | ||
| − | <math>\mathcal{F}(rect(\frac{t}{2})) = 2\sinc <math> | + | <math> \mathcal{F}(rect(\frac{t}{2})) = 2 sinc( 2 f) </math> |
| + | |||
| + | substituting the known transforms into <math>\quad (1)</math> | ||
| + | |||
| + | <math>X_(f) = \frac{1}{2} [\delta(f - \frac{1}{4}) + \delta(f + \frac{1}{4})] * 2 sinc( 2 f) </math> | ||
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| + | Evaluating the statement ( using sifting ) | ||
| + | |||
| + | <math>X_(f) = sinc(2 (f - \frac{1}{4}) + sinc( 2(f+\frac{1}{4})) | ||
Revision as of 11:03, 9 February 2009
Howdy, My name is Myron Lo and I'm a senior in EE.
I enjoy photography, combat sports, and Minidisc.
--Mlo 12:03, 13 January 2009 (UTC)
LaTex editor: http://thornahawk.unitedti.org/equationeditor/equationeditor.php
Experimenting with inserting formulas to participate in hw discussion
Hw1:
$ x_(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2}) \quad (1) $
Using the convolution property
$ X_(f) = \mathcal{F} (cos(\frac{\pi t}{2}))* \mathcal{F}(rect(\frac{t}{2})) $
where
$ \mathcal{F} (cos(\frac{\pi t}{2})) = \frac{1}{2} [\delta(f - \frac{1}{4}) + \delta(f + \frac{1}{4})] $
and
$ \mathcal{F}(rect(\frac{t}{2})) = 2 sinc( 2 f) $
substituting the known transforms into $ \quad (1) $
$ X_(f) = \frac{1}{2} [\delta(f - \frac{1}{4}) + \delta(f + \frac{1}{4})] * 2 sinc( 2 f) $
Evaluating the statement ( using sifting )
$ X_(f) = sinc(2 (f - \frac{1}{4}) + sinc( 2(f+\frac{1}{4})) $
