# lecture4 - Continuous-Time Convolution EE 313 Linear...

This preview shows pages 1–5. Sign up to view the full content.

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Continuous-Time Convolution EE 313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin 4 - 2 ( 29 ( 29 ( 29 ( 29 τ τ τ d t f f t f t f 2 1 2 1- ∫ ≡ ∞ ∞- Convolution Integral • Commonly used in engineering, science, math • Convolution properties – Commutative: f 1 ( t ) * f 2 ( t ) = f 2 ( t ) * f 1 ( t ) – Distributive: f 1 ( t ) * [ f 2 ( t ) + f 3 ( t )] = f 1 ( t ) * f 2 ( t ) + f 1 ( t ) * f 3 ( t ) – Associative: f 1 ( t ) * [ f 2 ( t ) * f 3 ( t )] = [ f 1 ( t ) * f 2 ( t )] * f 3 ( t ) – Shift: If f 1 ( t ) * f 2 ( t ) = c ( t ), then f 1 ( t ) * f 2 ( t - T ) = f 1 ( t - T ) * f 2 ( t ) = c ( t - T ). – Convolution with impulse, f ( t ) * δ ( t ) = f ( t ) – Convolution with shifted impulse, f ( t ) * δ ( t-T ) = f ( t-T ) important later in modulation 4 - 3 Graphical Convolution Methods • From the convolution integral, convolution is equivalent to – Rotating one of the functions about the y axis – Shifting it by t – Multiplying this flipped, shifted function with the other function – Calculating the area under this product – Assigning this value to f 1 ( t ) * f 2 ( t ) at t ( 29 ( 29 ( 29 ( 29 τ τ τ d t f f t f t f- ≡ ∫ ∞ ∞- 2 1 2 1 4 - 4 3 τ 2 f ( τ ) 2-2 + t 2 + t g ( t- τ ) * 2 2 t f ( t )-2 2 3 t g ( t ) Graphical Convolution Example...
View Full Document

{[ snackBarMessage ]}

### Page1 / 15

lecture4 - Continuous-Time Convolution EE 313 Linear...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online