# HW8S - ECE 402 Communications Engineering Homework 8 Solutions(Fall 2009 1 The carrier frequency should be located in the center of the band at f0

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ECE 402: Communications Engineering Homework 8 Solutions (Fall 2009) 1. The carrier frequency should be located in the center of the band at f 0 = (820 + 920) / 2 = 870 kHz. If the rolloﬀ is r = 0 . 5, the PSK signal bandwidth is W = 2(1 + r ) W N = 1 . 5 f b . For a channel bandwidth of 100 kHz, the symbol rate that uses the entire band is f b = 66 . 6 kbaud. The data rate is R = kf b where k is the number of bits/pulse. Since we require R = 200 kb/s, the signal constellation should have k = ( R/f b ) = 3 bits/pulse, or M = 2 k = 8 points. Thus, we should use 8-PSK. 2. (a) From the ﬁgure Z ( f ) = H c ( f ) X ( f ). Since z ( t ) = x ( t + T/ 4) + x ( t - T/ 4), we have Z ( f ) = F [ x ( t + T/ 4) + x ( t - T/ 4)] = ( e 2 πjfT/ 4 + e - 2 πjfT/ 4 ) X ( f ) = 2cos( πfT/ 2) X ( f ) , so H c ( f ) = Z ( f ) /X ( f ) = 2cos( πfT/ 2). (b) From G ( f ) = F [sinc(2 t/T )] = ( T/ 2)Π( Tf/ 2), the system pulse is P ( f ) = G ( f ) H c ( f ) H r ( f ) = ( T/ 2)Π( Tf/ 2) · 2cos( πfT/ 2) · cos(

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## This note was uploaded on 01/28/2012 for the course ECE 402 taught by Professor Townsend during the Fall '08 term at N.C. State.

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HW8S - ECE 402 Communications Engineering Homework 8 Solutions(Fall 2009 1 The carrier frequency should be located in the center of the band at f0

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