# HW3_Additional_problems - ) ( ) ( 4 4 4 3 3 3 2 2 2 1 1 1 t...

This preview shows page 1. Sign up to view the full content.

EE4501 - Homework 3: Additional problems NOTE: These two problems should be turned in along with problems 4.2-3 (a), (b), (c), (d); 4.2-8; 4.3-8; 4.8-1 from the textbook. Due date is Tue, Oct. 5, 2010. Problem 1: Consider a signal x ( t ) given as ) 2 sin( ) ( ) 2 cos( ) ( ) ( t f t x t f t x t x c Q c I where ) ( t x I and ) ( t x Q are the in-phase and quadrature components. (a) Show that ) ( t x can be written as )) ( 2 cos( ) ( ) ( t t f t E t x c where ) ( ) ( ) ( 2 2 t x t x t E Q I and )) ( / ) ( ( ) ( t x t x arctg t I Q . Find ) ( t E and ) ( t when x ( t ) is an AM signal. (b) Show that ) ( t x can be written as   t f j a c e t x t x 2 ) ( Re ) ( where ) ( ) ( ) ( t jx t x t x Q I a . Find ) ( t x a when x ( t ) is an SSB signal (USB and LSB). (Hint: use the definition of the Hilbert Transform in the frequency domain.) Problem 2. Four input signals ) ( ), ( ), ( ), ( 4 3 2 1 t x t x t x t x have been multiplexed to form a signal x ( t ) given as: ) 2 cos( ) ( ) 2 cos( ) ( ) 2 cos( ) ( ) 2 cos(
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) ( ) ( 4 4 4 3 3 3 2 2 2 1 1 1 t f t x t f t x t f t x t f t x t x All signals ) ( ), ( ), ( ), ( 4 3 2 1 t x t x t x t x are band-limited with bandwidth B . (a) Find conditions carrier frequencies 4 3 2 1 , , , f f f f and phase shifts 4 3 2 1 , , , should satisfy to guarantee that ) ( ), ( ), ( ), ( 4 3 2 1 t x t x t x t x can be demodulated while at the same time ) ( t x has bandwidth at most 4 B. (a) Sketch a demodulator that outputs ) ( ), ( ), ( ), ( 4 3 2 1 t x t x t x t x . Can we use envelope detectors to demodulate these signals? Explain your answer....
View Full Document

## This note was uploaded on 07/13/2011 for the course EE 4501 taught by Professor Ahmedtewfik during the Fall '10 term at Minnesota.

Ask a homework question - tutors are online