SPFirst-L25

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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 03/03/2010 for the course EE 48976 taught by Professor Nayak during the Spring '10 term at USC.

### Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online