| Line 11: | Line 11: | ||
Specify two different signals that satisfy these conditions. | Specify two different signals that satisfy these conditions. | ||
| − | + | Two signals that would satisfy these coniditions is the input signal | |
<math> | <math> | ||
| − | \ | + | \ x_1(t) = \sqrt{2} cos(2\pi t) |
| + | </math> | ||
| + | |||
| + | and | ||
| + | <math> | ||
| + | \ x_2(t) = - \sqrt{2} cos(2\pi t) | ||
</math> | </math> | ||
Revision as of 17:26, 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.
Two signals that would satisfy these coniditions is the input signal
$ \ x_1(t) = \sqrt{2} cos(2\pi t) $
and $ \ x_2(t) = - \sqrt{2} cos(2\pi t) $
