# sol1 - ECE 351, Systems I Jan. 21, 2009 OSU, Winter 2009...

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Unformatted text preview: ECE 351, Systems I Jan. 21, 2009 OSU, Winter 2009 Solutions - Problem Set 1 Problem 1 (a) 1 (b) 2 Problem 2 Problem 3 This discrete-time system replaces a sequence value by the average of three consecutive values. Armed with frequency analysis tools, we’ll soon see this smoothing filter to be a type of low-pass filter. (a) The system is a special case of the constant coefficient difference equation: y [ n ] =- X k a k y [ n- k ] + X k b k x [ n- k ] . Therefore, the system is linear and time-invariant. Note that the coefficients b k = 1 / 3 do not vary with time. The system is not recursive (all a k ’s are zero). (b) The system is causal because the output at time n depends only on the inputs at time n , n- 1 and n- 2. (c) Suppose the input is x [ n ] = δ [ n ]. Then, the output is given by y [ n ] = ( 1 3 n = 0 , 1 , 2 otherwise . That is, the output is the average of a “time-window” of three consecutive input samples, with the “window” centered at n- 1. The input samples are all zeros, except when the 3 window contains the sample at n = 0. The zero state response for= 0....
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## This note was uploaded on 05/05/2010 for the course ECE 351 taught by Professor Staff during the Spring '10 term at Ohio State.

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sol1 - ECE 351, Systems I Jan. 21, 2009 OSU, Winter 2009...

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