ECE-440_review1

ECE-440_review1 - Review for Spring 2011 ECE 440 Test 1...

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Unformatted text preview: Review for Spring 2011 ECE 440 Test 1 February 17, 2011 1 Test Specifics 1. No questions from lab (prelab, writeup, etc). Material will be from lecture. 2. No calculators, note sheets, or any other outside devices. 3. BE ABLE TO DO THE HOMEWORK PROBLEMS!!!! 2 Chapter 1 1. Block diagram of a communications system. 3 Chapter 2 1. All definitions in Section 2.1-2.2. 2. Understand AND be able to derive delta function properties on page 21-22 and from HW. 3. Know the definitions of continuous Fourier transform (CFT) and inverse CFT (e.g., X ( f ) = R - x ( t ) e- j 2 ft dt, etc.). Be able to prove F- 1 {F { x ( t ) }} = x ( t ) and F {F- 1 { X ( f ) }} = X ( f ) using integral expressions. 4. Know AND be able to show the symmetries of the CFT for real x ( t ) . 5. Be able to prove i.) linearity, ii.) X ( t ) x (- f ) if x ( t ) X ( f ) , iii.) X (- f ) x ( f ) if x ( t ) X ( f ) , iv.) time and frequency scaling, v.) time-shift and modulation, and vi.) time-shift and scaling. 6. Know the convolution integral. Also be able to show analytically (using integration prop- erties) that F { h ( t ) * x ( t ) } = F { h ( t ) }F { x ( t ) } . 7. Know and be able to prove Parsevals Theorem R | x ( t ) | 2 dt = R | X ( f ) | 2 df. 8. Know the functions and Fourier transform relations involving rect, sinc, triangle, sgn, and delta functions. 9. Know the definition of correlation (see text). 10. Know the definition of ( t ) . Know the time scaling property of ( t ) . 11. Know the definition of the complex Fourier series (CFS)....
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ECE-440_review1 - Review for Spring 2011 ECE 440 Test 1...

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