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<math> | <math> | ||
| − | \ x(t) = | + | \ x(t) = sqrt{2}sin(2\pit) |
</math> | </math> | ||
Revision as of 18:25, 26 September 2008
Suppose we are given the following information about a signal x(t):
1. x(t) is real and even.
2. x(t) is periodic with period T = 4 and Fourier coefficients $ \ a_k $.
3. $ \ a_k = 0 $ for $ \left \vert k \right \vert > 1 $.
4. $ \frac{1}{2}\int_{0}^{2} \left \vert x(t) \right \vert ^2 \, dt = 1 $.
Specify two different signals that satisfy these conditions.
One signal that would satisfy these coniditions is the input signal
$ \ x(t) = sqrt{2}sin(2\pit) $
