hw8 - 6.003 Homework 8 Due at the beginning of recitation...

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6.003 Homework 8 Due at the beginning of recitation on Wednesday, November 4, 2009 . Problems 1. CT stability Consider the following feedback system in which the box represents a causal LTI CT system that is represented by its system function. + K s 2 + s 2 X Y a. Determine the range of K for which this feedback system is stable. b. Determine the range of K for which this feedback system has real-valued poles. 2. DT stability Consider the following feedback system in which the box represents a causal LTI DT system that is represented by its system function. + K z 2 + z 2 X Y a. Determine the range of K for which this feedback system is stable. b. Determine the range of K for which this feedback system has real-valued poles. 3. BIBO stability A signal is said to be bounded if its absolute value is less than some constant at all times. A system is said to be stable in the bounded-input/bounded-output sense if all bounded inputs to the system generate bounded output signals. a. Let h [ n ] represent the unit-sample response of a DT LTI system. Determine the bounded input signal x [ n ] ( | x [ n ] | < B ) that maximizes the output y [ n ] at n = 0 . [Hint: look at the convolution sum.] b. Determine a rule based on h [ n ] to determine if a system is BIBO stable.
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