Problem 9.6 The signal m(t) = cos(2000πt) is transmitted by means of frequency modulation. If the frequency sensitivity kf is 2 kHz per volt, what is the Carson’s rule bandwidth of the FM signal. If the pre-detection SNR is 17 dB, calculate the post- detection SNR. Assume the FM demodulator includes an ideal low-pass filter with bandwidth 3.1 kHz. Solution The Carson Rule bandwidth is ( ) ( ) kHzfAkB mfT 82)1(222 =+=+= . Then from Eq.(9.59), 2 2 22 FM post 3 3 0 0 3 3 SNR 2 2 c f fc T T A k P k PA B N W N B W ⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠ We observed that the first factor is the pre-detection SNR, and we may write this as ( ) 2 1 FM FM 2 post pre 3 FM pre 3 2SNR SNR 8 3.1 SNR 1.61 ~ 19.2 dB ⎛ ⎞⋅⎜ ⎟= ⎜ ⎟⎝ ⎠ = × (There is an error in the answer given in the text.) 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.