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==Guessing a periodic signal based on a few properties given== | ==Guessing a periodic signal based on a few properties given== | ||
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| + | Properties: | ||
A) Fundamental Period = 2 | A) Fundamental Period = 2 | ||
B) <font size = '4'><math>a_0 = 0</math></font> | B) <font size = '4'><math>a_0 = 0</math></font> | ||
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| + | C) | ||
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| + | ==Finding the signal based on the properties== | ||
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| + | A) From A: | ||
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| + | N = 2. | ||
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| + | <math>x[n] = \sum_{k = 0}^{1} a_k e^{jk\pi n}</math> | ||
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| + | <math>a_k = \frac{1}{2} \sum_{n=0}^{1} x[n] e^{-jk\pi n}</math> | ||
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| + | B) From B: | ||
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| + | <math>a_0 = \frac{1}{2} \sum_{n=0}^{1} x[n] = 0</math> | ||
| + | |||
| + | Therefore 0.5x[0] + 0.5x[1] = 0 | ||
Revision as of 16:21, 26 September 2008
Guessing a periodic signal based on a few properties given
Properties:
A) Fundamental Period = 2
B) $ a_0 = 0 $
C)
Finding the signal based on the properties
A) From A:
N = 2.
$ x[n] = \sum_{k = 0}^{1} a_k e^{jk\pi n} $
$ a_k = \frac{1}{2} \sum_{n=0}^{1} x[n] e^{-jk\pi n} $
B) From B:
$ a_0 = \frac{1}{2} \sum_{n=0}^{1} x[n] = 0 $
Therefore 0.5x[0] + 0.5x[1] = 0
