{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw1_600

# hw1_600 - (d Say | a |< 1 Is the system stable(e What is...

This preview shows page 1. Sign up to view the full content.

ECE-600 Introduction to Digital Signal Processing Autumn 2011 Homework #1 Sep. 21, 2011 HOMEWORK ASSIGNMENT #1 Due Wed. Sep. 28, 2011 (in class) Problems: 1. Consider a discrete-time system H whose output, given input { x [ n ] } n = -∞ , is given by y [ n ] = 2 m =0 (3 - m ) x [ n - m ]. For parts (a)-(d), prove your claim using the properties summarized on page 4 of the lecture notes. (a) Is the system linear? (b) Is the system time-invariant? (c) Is the system causal? (d) Is the system stable? (e) What is the impulse response of the system? (f) What does the impulse response tell us about stability and causality? 2. Consider a discrete-time system H whose output, given input { x [ n ] } n = -∞ , is given by y [ n ] = x [ n ] - ay [ n - 1]. For parts (a)-(d), prove your claim using the properties summarized on page 4 of the lecture notes. (a) Is the system linear? (b) Is the system time-invariant? (c) Is the system causal?
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (d) Say | a | < 1. Is the system stable? (e) What is the impulse response of the system? (f) What does the impulse response tell us about stability and causality? 3. Consider a continuous-time system H c whose output, given input { x ( t ) } ∀ t , is given by y ( t ) = max d ∈ [ t,t-1) x ( d ). In other words, at time t , the output equals the maximum value of the input over the previous second. For parts (a)-(d), prove your claim using the properties summarized on page 4 of the lecture notes. (a) Is the system linear? (b) Is the system time-invariant? (c) Is the system causal? (d) Is the system stable? (e) What is the impulse response of the system? (f) What does the impulse response tell us about stability and causality? P. Schniter, 2011 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online