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From 1. we know that <math>x[n] = \frac{1}{6}\sum_{n=0}^{4}a_k e^{jk\frac{\pi}{3}n}\,</math> | From 1. we know that <math>x[n] = \frac{1}{6}\sum_{n=0}^{4}a_k e^{jk\frac{\pi}{3}n}\,</math> | ||
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| + | Using 2., it is apparent that this is the formula for <math>a_k\,</math>. Specifically, for <math>a_0\,</math> | ||
Revision as of 13:19, 25 September 2008
Guess the Periodic Signal
A certain periodic signal has the following properties:
1. N = 6
2. $ \sum_{n=0}^{4}x[n] = 4 $
3. $ \sum_{n=1}^{5}(-1)^nx[n] = 2 $
4. $ a_k = a_{k+3}\, $
Answer
From 1. we know that $ x[n] = \frac{1}{6}\sum_{n=0}^{4}a_k e^{jk\frac{\pi}{3}n}\, $
Using 2., it is apparent that this is the formula for $ a_k\, $. Specifically, for $ a_0\, $
