ECE130A-HW02-F10 - ECE 130A Signal Analysis and Processing...

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

View Full Document Right Arrow Icon
ECE 130A: Signal Analysis and Processing Prof. Michael Liebling Fall 2010 TAs: Jingning Han, Hari Sivakumar Distribution: Monday, 4 October 2010 Electrical & Computer Engineering Dept. Homework Due: Tuesday, 12 October 2010, 5:00PM University of California, Santa Barbara Homework 2 Problem 1: Impulse Response (20 points) Calculate the following integrals: (a) R -∞ x ( t ) δ ( t )d t (b) R -∞ x ( t ) δ ( t - 4)d t (c) R -∞ x ( t ) δ ( τ )d τ (d) R -∞ x ( τ ) δ ( t - τ )d τ (e) R -∞ δ ( t - τ )d τ (f) R -∞ x ( τ ) δ ( τ )d τ (g) R -∞ exp(j2 πτ ) δ ( τ - 1)d τ (h) R -∞ x ( t )( δ ( τ - 1) - δ ( τ + 1))d τ Problem 2: Convolution (20 points) For each of the following pairs of waveforms, use the convolution integral to find the response y ( t ) of the LTI system with impulse response h ( t ) to the input x ( t ). Sketch your results. (a) x ( t ) = I [1,3] ( t ) = ( 1, 1 t 3 0 otherwise, and h ( t ) = ( ( t - 1) 3 , 1 t 2 0 otherwise. (b) x ( t ) = exp( - α t ) u ( t ) and h ( t ) = exp( - β t ) u ( t ), (assuming α 6= β ).
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ 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