SPFirst-L24

SPFirst-L24 - Signal Processing First LECTURE OBJECTIVES...

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4/19/2005 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 24 Amplitude Modulation (AM) 4/19/2005 © 2003, JH McClellan & RW Schafer 3 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 4/19/2005 © 2003, JH McClellan & RW Schafer 4 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 ( ω−ω 0 )) Delay Property Frequency Shifting Linearity Property x ( at ) 1 | a | X ( j ( a )) Scaling 4/19/2005 © 2003, JH McClellan & RW Schafer 5 Table of FT Properties x ( t ) h ( t ) H ( j ) 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
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4/19/2005 © 2003, JH McClellan & RW Schafer 6 Frequency Shifting Property e j ω 0 t x ( t ) e j t dt −∞ = x ( t ) e j ( 0 ) t dt −∞ = X ( j ( ω−ω 0 )) x ( t ) e j 0 t X ( j ( 0 )) y ( t ) = sin 7 t π t e j 0 t Y ( j ) = 1 0 7 < < 0 + 7 0 elsewhere 4/19/2005 © 2003, JH McClellan & RW Schafer 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 ) 4/19/2005 © 2003, JH McClellan & RW Schafer 8 Cosine Input to LTI System Y ( j ) = H ( j
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SPFirst-L24 - Signal Processing First LECTURE OBJECTIVES...

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