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

Revision as of 17:39, 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} \! $

Answer

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