1 / 19

Examples of Convolution

Examples of Convolution. 3.2. Graphical Examples. Impulse Response of an Integrator circuit due to the unit impulse function Response of an integrator due to a unit step function Response of an Integrator circuit due to the unit ramp input

prem
Download Presentation

Examples of Convolution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Examples of Convolution 3.2

  2. Graphical Examples • Impulse Response of an Integrator circuit due to the unit impulse function • Response of an integrator due to aunit step function • Response of an Integrator circuit due to the unit ramp input • Response of an integrator due to a rectangular pulse

  3. Impulse Response of an Integrator =δ(t) d(τ) d(τ) 0 0 interval of integration interval of integration

  4. Graphical Examples • Impulse Response of an Integrator circuit due to the unit impulse function • Response of an integrator due to aunit step function • Response of an Integrator circuit due to the unit ramp input • Response of an integrator due to a rectangular pulse

  5. Response of an Integrator Due to a Unit Ramp Function =tu(t) Why is h(t)=u(t)?

  6. Response of an Integrator Due to a Unit Step Function =tu(t) Constant!

  7. Graphical Illustration (t=-1) No area of intersection

  8. Graphical Illustration (t=1)

  9. Response of an Integrator Due to a Unit Step Function =tu(t) Unit step function is only 1 when the argument is greater than 0. It does not make sense to integrate all the way to infinity.

  10. A system with rectangular impulse response u(t) δ(t) u(t-2)

  11. Example (why not take advatage of linearity?)

  12. Focus on x1(t) δ(t)→h(t) δ(t+3)→h(t+3)

  13. Understanding h(t-τ)

  14. h(t-τ) when t=-1 h(τ) h(-1+τ) h(-1-τ)

  15. Integration when t<0 h(t-τ) for t<0

  16. h(t-τ) when t=0.5 h(τ) h(0.5-τ) h(0.5+τ)

  17. Integration when 0<t<2 h(t-τ) for 0<t<2 (move to the right as t increases)

  18. h(t-τ) when t=3.5 h(τ) h(3.5+τ) h(3.5-τ) 3.5 3.5-2

  19. Integration when t>2 t-2 t

More Related