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| − | <math>\ x(t) = \frac{-1}{4}(e^{5(j2\pi t)} - e^{-1(j2\pi t)} - e^{1(j2\pi t)} + e^{-5(j2\pi t)}</math> | + | <math>\ x(t) = \frac{-1}{4}(e^{5(j2\pi t)} - e^{-1(j2\pi t)} - e^{1(j2\pi t)} + e^{-5(j2\pi t)})</math> |
| − | <math>a_{5} = \frac{-1}{4}, a_{-1} = \frac{1}{4}, a_{1} = \frac{1}{4}, a_{-5} = \frac{-1}{4} | + | <math>a_{5} = \frac{-1}{4}, a_{-1} = \frac{1}{4}, a_{1} = \frac{1}{4}, a_{-5} = \frac{-1}{4}</math> |
All other values <math>\ a_{n} = 0</math> | All other values <math>\ a_{n} = 0</math> | ||
Revision as of 07:18, 26 September 2008
$ \ x(t) = \sin(4\pi t) \sin(6\pi t) $
$ \ x(t) = (\frac{e^{j4\pi t} - e^{-j4\pi t}}{2}) (\frac{e^{j6\pi t} - e^{-j6\pi t}}{2j}) $
$ \ x(t) = \frac{-1}{4}(e^{j10\pi t} - e{-j2\pi t} - e^{j2\pi t} + e^{-j10\pi t}) $
$ \ x(t) = \frac{-1}{4}(e^{5(j2\pi t)} - e^{-1(j2\pi t)} - e^{1(j2\pi t)} + e^{-5(j2\pi t)}) $
$ a_{5} = \frac{-1}{4}, a_{-1} = \frac{1}{4}, a_{1} = \frac{1}{4}, a_{-5} = \frac{-1}{4} $
All other values $ \ a_{n} = 0 $
