e1sample.pdf - 332:345 – Linear Systems Signals – Fall...

This preview shows page 1. Sign up to view the full content.

332:345 – Linear Systems & Signals – Fall 2009 Sample Exam-1 Questions 1. The impulse response h(t) of an LTI system and an input signal f(t) are nonzero over the following time ranges: h(t), a t b f(t), c t d The corresponding output is given by the convolutional equation: y(t) = h(t τ)f(τ)dτ Determine the time range for y(t) , and the precise limits of the above integral. 2. Sketch the two signals h(t) = e t u(t) and f(t) = u(t) u(t 5 ) . Then, determine their convolution y(t) = h(t τ)f(τ)dτ using the following two methods: (a) By performing the indicated time integration. (b) By working with Laplace transforms. 3. Using Laplace transforms, solve the following differential equation, ¨ y(t) + 5 ˙ y(t) + 4 y(t) = 3 f(t) where f(t) = e 3 t u(t) with arbitrary initial conditions: y( 0 ) and ˙ y( 0 ) . Identify the parts of the solution that correspond to the decomposition of y(t) into a “homogeneous solution" and a “particular solution”. Similarly,
Image of page 1
You've reached the end of this preview.
  • Fall '11
  • Zoran

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern