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3. <math> \ a_k = 0 </math> for <math> \left \vert k \right \vert > 1 </math>. | 3. <math> \ a_k = 0 </math> for <math> \left \vert k \right \vert > 1 </math>. | ||
| − | 4. <math> \frac{1}{2}\int_{0}^{2} \left \vert x(t) \right \vert ^2 \, dt = 2. </math> | + | 4. <math> \frac{1}{2}\int_{0}^{2} \left \vert x(t) \right \vert ^2 \, dt = 3.2. </math> |
Specify two different signals that satisfy these conditions. | Specify two different signals that satisfy these conditions. | ||
Revision as of 17:22, 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 = 3.2. $
Specify two different signals that satisfy these conditions.
One signal that would satisfy these coniditions is the input signal
$ \ x(t) = x(-t) = t^2 $
