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Unformatted text preview: EE102 Discussion 5 2010-10-26 vasiliy karasev System Properties 1. System has impulse response h [ n ] = 2 n u [- n ] Is the system stable? Is the system causal? Notice that h [ n ] = 0 for all n > and h [ n ] 6 = 0 for all n . When n < , 2 n < 1 . Observe that h  = 1 , h [- 1] = 1 2 , h [- 2] = 1 4 , h [- 3] = 1 8 ,... This is a geometric series that grows from n - . Being a geometric series, it is convergent, and you can write X n =- | h [ n ] | < Consider also what happens when you time reverse h[n] (only for purposes of determining stability!). Whether of not the sequence is absolutely summable should not change because of the time reversal (amplitudes are not altered in any way). When you do the time reversal, h [ n ] = 2- n u [ n ] = 1 2 n u [ n ] , which you recognize as the convergent sequence (geometric series again). System is stable. For an LTI system to be causal, it must be that h [ n ] = 0 for n < . This is the condition that prevents the system from looking ahead in time, at future values of the input signal. Given impulse response clearly fails this criterion. System is not causal. 2. System has impulse response h [ n ] = [ n ]- [ n- 1] Is the system memoryless? Is it causal? h [ n ] = 0 for n < , so causal. If a system is memoryless it may not look at f uture or p ast values of input. For given system, current output depends on past values of x [ n...
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- Fall '08