lecture13 - EE313 Linear Systems and Signals Fall 2010...

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Unformatted text preview: EE313 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 Fourier Transform Properties 13 - 2 ( 29 ( 29 ∫ ∞ ∞-- = dt e t f F t j ϖ ϖ ( 29 ( 29 ∫ ∞ ∞- = ϖ ϖ π ϖ d e F t f t j 2 1 ( 29 ( 29 ϖ F t f ↔ ( 29 ( 29 ϖ π- ↔ f t F 2 1 τ /2- τ /2 t f ( t ) τ ϖ F ( ϖ )-6 π τ-4 π τ- 2 π τ 2 π τ 4 π τ 6 π τ Duality • Forward/inverse transforms are similar • Example: rect(t/ τ ) ↔ τ sinc( ϖ τ / 2) Apply duality τ sinc(t τ /2) ↔ 2 π rect(- ϖ / τ ) rect(·) is even τ sinc(t τ /2) ↔ 2 π rect( ϖ / τ ) 13 - 3 Scaling • Given and that a ≠ | a | > 1: compress time axis, expand frequency axis | a | < 1: expand time axis, compress frequency axis • Extent in time domain is inversely proportional to extent in frequency domain (a.k.a bandwidth) f ( t ) is wider ↔ spectrum is narrower ( 29 ( 29 ϖ F t f ↔ ( 29 ↔ a F a at f ϖ 1 13 - 4...
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This note was uploaded on 02/16/2011 for the course ECE 313 taught by Professor Evans during the Spring '11 term at University of Texas.

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lecture13 - EE313 Linear Systems and Signals Fall 2010...

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