SPFirst-L25

SPFirst-L25 - 8/22/2003 © 2003, JH McClellan & RW...

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Unformatted text preview: 8/22/2003 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 25 Sampling and Reconstruction (Fourier View) 8/22/2003 © 2003, JH McClellan & RW Schafer 3 LECTURE OBJECTIVES ¡ Sampling Theorem Revisited ¡ GENERAL: in the FREQUENCY DOMAIN ¡ Fourier transform of sampled signal ¡ Reconstruction from samples ¡ Reading: Chap 12, Section 12-3 ¡ Review of FT properties ¡ Convolution ÅÆ multiplication ¡ Frequency shifting ¡ Review of AM 8/22/2003 © 2003, JH McClellan & RW Schafer 4 Table of FT Properties x ( t − t d ) ⇔ e − j ω t d X ( j ω ) x ( t ) e j ω t ⇔ X ( j ( ω −ω )) Delay Property Frequency Shifting x ( at ) ⇔ 1 | a | X ( j ( ω a )) Scaling x ( t ) ∗ h ( t ) ⇔ H ( j ω ) X ( j ω ) 8/22/2003 © 2003, JH McClellan & RW Schafer 5 Amplitude Modulator ¡ x(t) modulates the amplitude of the cosine wave. The result in the frequency-domain is two SHIFTED copies of X(j ω ). y ( t ) = x ( t )cos( ω c t + ϕ ) X ( j ω ) x ( t ) cos( ω c t + ϕ ) Y ( j ω ) = 1 2 e j ϕ X ( j ( ω −ω c )) + 1 2 e − j ϕ X ( j ( ω + ω c )) Phase 8/22/2003 © 2003, JH McClellan & RW Schafer 6 DSBAM: Frequency-Domain “Typical” bandlimited input signal Frequency-shifted copies )) ( ( 2 1 c j j X e ω ω ϕ + − )) ( ( 2 1 c j j X e ω ω ϕ − Upper sideband Lower sideband ) ( ω j X 8/22/2003...
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This note was uploaded on 03/03/2010 for the course EE 48976 taught by Professor Nayak during the Spring '10 term at USC.

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SPFirst-L25 - 8/22/2003 © 2003, JH McClellan & RW...

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