{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ecen314-lec5 - Lecture 5 DT Convolution Tie Liu 1 LTI...

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

View Full Document Right Arrow Icon
Lecture 5: DTConvolution Tie Liu September 13, 2011 1 LTI systems Recall that a CT system is TI if x ( t ) y ( t ) = x ( t t 0 ) y ( t t 0 ) , t 0 R and that it is linear x 1 ( t ) y 1 ( t ) and x 2 ( t ) y 2 ( t ) = ax 1 ( t ) + bx 2 ( t ) ay 1 ( t ) + by 2 ( t ) , a, b R For ECEN 314, we shall focus on systems that are both linear and time invariant (LTI): Practical importance. The powerful analysis tools associated with LTI systems. A basic fact: If we know the response of an LTI system to some inputs, we actually know the response to many inputs. Question: What is the smallest set of inputs for which, if we know their outputs, we can determine the output of any input signal? 2 DT Convolution For DT systems, the answer is surprisingly simple: All we need to know is the response (denoted by h [ n ]) to the unit impulse function δ [ n ] = braceleftbigg 1 , n = 0 0 , n negationslash = 0 Signal decomposition using the unit impulse function and its shifts: x [ n ] = summationdisplay k = -∞ x [ k ] δ [ n k ] 1
Image of page 1

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

View Full Document Right Arrow Icon
-1 -2 0 1 2 x [ n ] n -2 n -1 n 0 n 1 n 2 n x [ -
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