Problem 9.1 In practice, we often cannot measure the signal by itself but must measure the signal plus noise. Explain how the SNR would be calculated in this case. Solution Let r(t) = s(t) + n(t) be the received signal plus noise. Assuming the signal is independent of the noise, we have that the received power is [ ] ( )[ ][ ] [ ] [ ][ ] [ ] [ ] [ ] NS tntntsts tntntsts tnts trR ++= ++= ++= += = 0 )()()(2)( )()()(2)( )()( )( 22 22 2 2 0 EEEE EEE E E where S is the signal power and N is the average noise power. We then measure the noise alone [ ] N tnR = = )(21 E and the SNR is given by 1 10SNR R RR \u2212= Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.