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Problem 9.17. The signal ( ) cos(400 )m t t\u3c0= is transmitted via FM. There is an ideal band-pass filter passing 100 \u2264 |f| \u2264 300 at the discriminator output. Calculate the post- detection SNR given that kf = 1 kHz per volt, and the pre-detection SNR is 500. Use Carson\u2019s rule to estimate the pre-detection bandwidth. Solution We begin by estimating the Carson\u2019s rule bandwidth ( ) ( ) Hz2400 200)1(10002 2 = += += mfT fAkB We are given that the pre-detection SNR is 500. From Section 9.7 this implies 2400 1 2 500 2 0 2 0 2 N A BN ASNR c T cFM pre = = Re-arranging this equation, we obtain Hz102.1 2 6 0 2 ×= N Ac The nuance in this problem is that the post-detection filter is not ideal with unity gain from 0 to W and zero for higher frequencies. Consequently, we must re-evaluate the post- detection noise using Eq. (9.58) [ ] 7 2 0 33 2 0 300 100 2 100 300 2 2 0 106.2 3 2 100300 3 2 powernoisedetection-postAvg. ×= \u2212= \u23a5\u23a6 \u23a4\u23a2\u23a3 \u23a1 += \u222b\u222b\u2212 \u2212 c c c A N A N dffdff A N The post-detection SNR then becomes Continued on next slide 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. Problem 9.17 continued ( ) ( )( ) 8.69230 106.2 5.01000102.13 106.22 3 106.22 3 SNR 7 2 6 7 2 0 2 7 0 22 FM post = ××= ×\u239f\u239f\u23a0 \u239e \u239c\u239c\u239d \u239b= ×= Pk N A N PkA fc fc where we have used the fact that kf = 1000 Hz/V and P = 0.5 watts. In decibels, the post- detection SNR is 48.4 dB. 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.