convolution
Download
Skip this Video
Download Presentation
Convolution

Loading in 2 Seconds...

play fullscreen
1 / 3

Convolution - PowerPoint PPT Presentation


  • 121 Views
  • Uploaded on

Convolution. LTI: h(t). LTI: h[n]. g(t). g[n]. g(t)  h(t). g[n]  h[n]. Example: g[n] = u[n] – u[3-n] h[n] =  [n] +  [n-1]. Convolution methods:. Method 1: “running sum” Plot x and h vs. m Flip h over vertical axis to get h[-m] Shift h[-m] to obtain h[n-m]

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Convolution' - trella


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
convolution
Convolution

LTI:

h(t)

LTI:

h[n]

g(t)

g[n]

g(t)  h(t)

g[n]  h[n]

Example: g[n] = u[n] – u[3-n]

h[n] = [n] + [n-1]

convolution methods
Convolution methods:
  • Method 1: “running sum”
    • Plot x and h vs. m
    • Flip h over vertical axis to get h[-m]
    • Shift h[-m] to obtain h[n-m]
    • Multiply to obtain x[m]h[n-m]
    • Sum on m, m x[m] h[n-m]
    • Increment n and repeat steps 3~6
convolution methods1
Convolution methods:
  • Method 2: Superposition method
    • We know [n]  h[n] and the system is LTI.
    • Therefore, a0[n-n0]  a0h[n-n0]
    • a0[n-n0] + a1[n-n1] + …  a0h[n-n0] + a1h[n-n1] …
    • Since the input can be expressed as a sum of shifted unit samples:

x[n] = … x[-2][n+2] + x[-1][n+1] + x[0][n] + x[1][n-1] + …

    • The out is then a sum of shifted unit sample responses:

x[n0][n-n0] + x[n1][n-n1] + …  x[n0]h[n-n0] + x[n1]h[n-n1] …

 1k=-1x[k]h[n-k]

(The Convolution Sum!)

ad