Convolution (Widescreen).pptx - CONVOLUTION A GRAPHICAL...

  • No School
  • AA 1
  • 42

This preview shows page 1 - 11 out of 42 pages.

CONVOLUTION A GRAPHICAL APPROACH Adrian Gonzalez April 24, 2019 CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 1

Subscribe to view the full document.

STEPS TO EVALUATE THE CONVOLUTION INTEGRAL: 1. Conversion : Replace with dummy variable for each of the signals. 2. Folding : Take a mirror image of about the ordinate axis to obtain . 3. Displacement : Shift or delay by to obtain . 4. Multiplication : Find the product of and . 5. Integration : For a given time , calculate the area under the product for to get at . CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 2
EXAMPLE 1 Find the convolution of the two signals shown below: 0 1 ? 1 ( ? ) ? 0 1 2 3 ? 2 ( ? ) ? 2 1 CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 3

Subscribe to view the full document.

CONVERSION Replace with . 0 1 ? 1 ( ? ) ? 2 0 1 2 3 ? 2 ( ? ) ? 1 CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 4
DISPLACEMENT Since the convolution is commutative, we can fold either signal, thus lets fold : 0 1 ? 1 ( ? ) ? 0 1 ? 1 ( ? ) ? -1 2 CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 5

Subscribe to view the full document.

DISPLACEMENT (CONT.) The signal can now be shifted or delayed by : 0 1 ? 1 ( ? ? ) ? -1 ? 1 ? 2 CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 6
PROCESS: For : No overlap. Note : There will be partial overlap for . ? ( ? ) = ? 1 ( ? ) ∗? 2 ( ? ) = 0 0 1 ? -1 2 3 4 ? 2 ( ? ) 2 1 ? 1 ? ? 1 ( ? ? ) CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 7

Subscribe to view the full document.

PROCESS (CONT.): For : There’s partial overlap. Note : There will be full overlap for . ? ( ? ) = 1 ? ( 2 ) ( 1 ) ? ? = 2 ? 2 0 1 ? -1 2 3 4 ? 2 ( ? ) 2 1 ? 1 ? ? 1 ( ? ? ) CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 8
PROCESS (CONT.): For : There’s complete overlap. Note : There will partial overlap once again for . ? ( ? ) = ? 1 ? ( 2 ) ( 1 ) ? ? = 2 0 1 ? -1 2 3 4 ? 2 ( ? ) 2 1 ? 1 ? ? 1 ( ? ? ) CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA | ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT
Image of page 9

Subscribe to view the full document.

PROCESS (CONT.): For : There’s partial overlap.
Image of page 10
Image of page 11

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

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes