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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 6

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online