102_1_hw7_soln

102_1_hw7_soln - 1 EE102 Fall Quarter 2011 Systems and...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 EE102 Systems and Signals Fall Quarter 2011 Jin Hyung Lee Homework #7 Due: Not Handed In 1. Practical Signal Reconstruction If we have a samples of a bandlimited signal sampled at the Nyquist rate, we can per- fectly reconstruct the signal by passing the sequence of impulses through a lowpass filter. However, the impulse train is not a realizable signal. In this problem we will look at the case where we approximate the impulses by short rectangular pulses, and see what effect this has on the reconstructed signal. The ideal sampled signal, sampled at an interval of T , is 2T -T -3T -2T T 0 3T t Ideal Sampled Signal ¯ f ( t ) = n = - f ( nT ) δ ( t - nT ) If we approximate the impulses with rects, the signal looks like 2T -T -3T -2T T 0 3T t Approximate Sampled Signal ˜ f ( t ) = n = - f ( nT ) p ( t - nT ) where the rect we are using to approximate the impulses is -T T 0 t p ( t ) = rect ( 4 t / T ) (a) Write an expression for ˜ f ( t ) in terms of ¯ f ( t ) , using the definition of p ( t ) . Solution: The approximate sampled signal is the ideal sampled signal convolved with the rect we are using to approximate the impulse ˜ f ( t ) = ¯ f ( t ) * rect(4 t/T ) .
Image of page 1

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

View Full Document Right Arrow Icon
2 (b) Find an expression for ˜ F ( ) in terms of ¯ F ( ) .
Image of page 2
Image of page 3
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