hw1_600(2)

# hw1_600(2) - (a Is the system linear(b Is the system...

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ECE-600 Introduction to Digital Signal Processing Autumn 2010 Homework #1 Sept. 22, 2010 HOMEWORK ASSIGNMENT #1 Due Wed. Sept. 29, 2010 (in class) Problems: 1. Consider a discrete-time system H whose output, given input { x [ n ] } n = -∞ , is given by y [ n ] = 0 m = - 2 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 continuous-time system H c whose output, given input { x ( t ) } t , is given by y ( t ) = Im { x ( t ) } . Inotherwords,theimaginarypartoftheinputisretainedandtherealpartisdiscarded. Forparts(a)-(d), proveyourclaimusingthepropertiessummarizedonpage4ofthelecturenotes. (a) Is the system linear?
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Unformatted text preview: (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? 3. Consider a discrete-time system H whose output, given input { x [ n ] } ∞ n =-∞ , is given by y [ n ] = x [ n ] + ay [ n-2]. For parts (a)-(d), prove your claim using the properties summarized on page 4 of the lecture notes. (Hint: The input/output relationship can be recursively deduced.) (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? P. Schniter, 2010 1...
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