hw1_600 - the lecture notes. (a) Is the system linear? (b)...

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

View Full Document Right Arrow Icon
ECE-600 Introduction to Digital Signal Processing Winter 2011 Homework #1 Jan. 5, 2011 HOMEWORK ASSIGNMENT #1 Due Wed. Jan. 12, 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 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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the lecture notes. (a) Is the system linear? (b) Is the system time-invariant? (c) Is the system causal? (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 ) = d dt x ( t ), i.e., the derivative (or slope) of x ( t ). 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? P. Schniter, 2011 1...
View Full Document

Ask a homework question - tutors are online