2025-L20su10

2025-L20su10 - ECE2025 Summer 2010 Lecture 20 Amplitude...

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1 7/9/2010 1 ECE2025 Summer 2010 Lecture 20 Amplitude Modulation (AM) 21 Jul 10 Guest Lecturer: David Taylor 7/9/2010 3 ANNOUNCEMENTS ± HW #9 due July 26-27 ± Do Lab #10 on July 28-29 ± All in-lab ± We’ve set aside time in lab for you to fill out the the GaTech course survey for ECE2025 7/9/2010 4 LECTURE OBJECTIVES ± Review of FT properties ± Convolution <--> multiplication ± Frequency shifting ± Sinewave Amplitude Modulation ± AM radio ± Frequency-division multiplexing ± FDM ± Reading: Chapter 12, Section 12-2 7/9/2010 5 Table of Easy FT Properties ax 1 ( t ) + bx 2 ( t ) aX 1 ( j ω ) + bX 2 ( j ) x ( t t d ) e j t d X ( j ) x ( t ) e j 0 t X ( j ( 0 )) Delay Property Frequency Shifting Linearity Property x ( at ) 1 | a | X ( j ( a )) Scaling
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2 7/9/2010 6 Table of FT Properties x ( t ) h ( t ) H ( j ω ) X ( j ) x ( t ) e j 0 t X ( j ( 0 )) x ( t ) p ( t ) 1 2 π X ( j ) P ( j ) dx ( t ) dt ( j ) X ( j ) Differentiation Property 7/9/2010 7 Convolution Property ± Convolution in the time-domain corresponds to MULTIPLICATION MULTIPLICATION in the frequency-domain y ( t ) = h ( t ) x ( t ) = h ( τ ) −∞ x ( t ) d Y ( j ) = H ( j ) X ( j ) y ( t ) = h ( t ) x ( t ) x ( t ) Y ( j ) = H ( j ) X ( j ) X ( j ) 7/9/2010 8 Cosine Input to LTI System Y ( j ) = H ( j ) X ( j ) = H ( j )[ πδ ( 0 ) + ( + 0 )] = H ( j 0 ) ( 0 ) + H ( j 0 ) ( + 0 ) y ( t ) = H ( j 0 ) 1 2 e j 0 t + H ( j 0 ) 1 2 e j 0 t = H ( j 0 ) 1 2 e j 0 t + H * ( j 0 ) 1 2 e j 0 t = H ( j 0 ) cos( 0 t +∠ H ( j 0 )) 7/9/2010 9 Ideal Lowpass Filter H lp ( j ) co co y ( t ) = x ( t ) if 0 < co y ( t ) = 0 if 0 > co
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3 7/9/2010 10 The way communication systems work
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2025-L20su10 - ECE2025 Summer 2010 Lecture 20 Amplitude...

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