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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern