midterm1 - Digital Signal Processing I(ECE 410 Summer II...

Info iconThis preview shows pages 1–3. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Digital Signal Processing I (ECE 410, Summer II 2009) University of Illinois at Urbana-Champaign Electrical and Computer Engineering Midterm 1 1. Answer the following questions. Justify your answer briefly. (a) (5 points) Is this system causal? y [ n ] = x [- n ] . (1) (b) (5 points) Is this system time-invariant (or shift-invariant)? y [ n ] = h [ n ] * x [ n ] , (2) where * is a linear convolution. (c) (5 points) Is this system stable? H ( z ) = 1 ( 1 + 1 100 z- 2 ) (1- 2000 z- 2 ) , anticausal (3) 2. (20 points) The discrete sequence x [ n ] is given by x [ n ] = ‡ 1 √ 2 · n n = 0 , 2 , 4 , 6 , 8 , ··· , ∞ n 4 n =- 1 , 1 , 3 , 5 otherwise (4) Let X d ( ω ) be the DTFT of x [ n ]. (a) Find X d (0). (b) Find X d ( π ). (c) Find R π- π | X d ( ω ) | 2 dω (d) Consider an LTI system whose impulse response h[n] is x [- n ]. Let y [ n ] be the output of the system for the input x [ n ]. Find R π- π Y d ( ω ) dω . 3. (20 points) A block diagram of a causal LTI system is depicted below;3....
View Full Document

Page1 / 3

midterm1 - Digital Signal Processing I(ECE 410 Summer II...

This preview shows document pages 1 - 3. Sign up to view the full document.

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