Difference Equation and Dirac Delta

AI Thread Summary
The discussion revolves around solving the difference equation y[n] - (2/3)y[n-1] = x[n] with x[n] being the Dirac delta function. The initial attempt mistakenly assumes y[n-1] equals the Dirac delta function shifted by one. The correct solution is y[n] = (2/3)^{n}U[n], where U[n] is the unit step function. Participants seek clarification on how to derive this solution from the given equation. The conversation emphasizes understanding the properties of difference equations and the role of the Dirac delta function in such contexts.
Larrytsai
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Homework Statement



y[n] - (2/3)y[n-1] = x[n]

what is y[n] if x[n] = diracdelta[n]


The Attempt at a Solution



for some reason, i argued that y[n-1] = diracdelta[n-1]

so

y[n] = diracdelta[n] + (2/3)diracdelta[n-1]

Im pretty sure this is wrong, anybody can help?
 
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The answer is y[n] = (\frac{2}{3})^{n}U[n]
 
You mind explaining how you got to what y[n] is?
 

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