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==Guess the Periodic Signal== | ==Guess the Periodic Signal== | ||
| + | Find a DT signal that satisfies these properties: | ||
| + | 1. period N=2 | ||
| + | |||
| + | 2. <math>\sum_{n=0}^3 x[n] = 2</math> | ||
| + | |||
| + | 3. <math>a_1=3 \!</math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | 1. a period of 2 gives us | ||
| + | |||
| + | <math>x[n] = \frac{1}{2}\sum_0^{N-1} a_ke^{jk\pi n}</math> | ||
| + | |||
| + | 2. <math>a_0 = 1 \!</math> | ||
| + | |||
| + | 3. <math>a_1 = 3 \!</math> | ||
| + | |||
| + | Giving us: | ||
| + | |||
| + | <math>x[n] = 1 + 3e^{j\pi n} \!</math> | ||
==Answer== | ==Answer== | ||
Revision as of 16:39, 26 September 2008
Guess the Periodic Signal
Find a DT signal that satisfies these properties:
1. period N=2
2. $ \sum_{n=0}^3 x[n] = 2 $
3. $ a_1=3 \! $
Solution
1. a period of 2 gives us
$ x[n] = \frac{1}{2}\sum_0^{N-1} a_ke^{jk\pi n} $
2. $ a_0 = 1 \! $
3. $ a_1 = 3 \! $
Giving us:
$ x[n] = 1 + 3e^{j\pi n} \! $
