hw1_600 - (d) Say | a | < 1. Is the system stable? (e)...

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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?
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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...
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This note was uploaded on 10/29/2011 for the course ECE 600 taught by Professor Clymer,b during the Fall '08 term at Ohio State.

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