Assume there's a Finite Impulse Response (FIR) filter with three zeros locate at e -√2, while three poles locate at the origin. e¹, e- and 4, a. Find its transfer function. b. Determine if this filter is stable (why or why not?). c. Find and sketch its impulse response.

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Assume there's a Finite Impulse Response (FIR) filter with three zeros locate at ee- and
-√2, while three poles locate at the origin.
4, 4
a. Find its transfer function.
b. Determine if this filter is stable (why or why not?).
c. Find and sketch its impulse response.
Transcribed Image Text:Assume there's a Finite Impulse Response (FIR) filter with three zeros locate at ee- and -√2, while three poles locate at the origin. 4, 4 a. Find its transfer function. b. Determine if this filter is stable (why or why not?). c. Find and sketch its impulse response.
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in the question there is a zero at -sqrt(2) but in the answers its not written as a negative but a positive, so in the equation it ends up being (z - sqrt(2)) rather than (z + sqrt(2)), are you able to expain why its not a negative?

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in part a are you able to explain or show the steps where the j's cancel out from (z-1/sqrt(2)+j1/sqrt(2))(z-1/sqrt(2)-j1/sqrt(2)) to (z-1/sqrt(2))^2+(1/sqrt(2))^2 

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