# hw9 - ECE130B March 1 2010 Homework 9 Due Date March 8 2010...

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ECE130B March 1, 2010 Homework 9 Due Date : March 8, 2010 Reading : Chapter 10 of the text book. Inverse system . Given a system A, its inverse is a system B, such that the cascade of the two systems acts as the identity system. By this we mean that for any input signal x [ n ] , for which the output of system A is well-defined, the output of the cascade of A and B should be just x [ n ] . Exercise 1. The input x [ n ] and output y [ n ] of an LTI system satisfy the relationship y [ n +4] - y [ n - 4]= x [ n ] . A) Draw a discrete circuit that could realize this system. B) Find the impulse response h [ n ] , if the system is causal. Is the system stable? If not, can you find a bounded input signal for which the output signal grows unboundedly? Hint : You can find the impulse response directly without using zero-input reponses. C) Find the impulse response h [ n ] if the system is anti-causal (that is h [ n ] = 0 for n > 0 ). Is the system stable? D) Find the system transfer function H ( z ) and all of its poles and zeros. Can the system be stable?
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