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Problem 9.18. Suppose that the spectrum of a modulating signal occupies the frequency band 1 2f f f\u2264 \u2264 . To accommodate this signal, the receiver of an FM system (without pre-emphasis) uses an ideal band-pass filter connected to the output of the frequency discriminator; the filter passes frequencies in the interval 1 2f f f\u2264 \u2264 . Determine the output signal-to-noise ratio and figure of merit of the system in the presence of additive white noise at the receiver input. Solution Since the post detection filter is no longer an ideal brickwall filter, we must revert to Eq. (9.58) to compute the post-detection noise power. For this scenario (similar to Problem 9.17) [ ]313220 22 2 0 3 2 powernoisedetection-postAvg. 2 1 1 2 ff A N dffdff A N c f f f fc \u2212= \u23a5\u23a5\u23a6 \u23a4 \u23a2\u23a2\u23a3 \u23a1 += \u222b\u222b \u2212 \u2212 Since the average output power is still , the post detection SNR is given by Pk f 2 ( )31320 22 2 3 ffN PkA SNR fcFMpost \u2212= For comparison purposes, the reference SNR is 2 0 2 12 ( ) c ref ASNR N f f = \u2212 The corresponding figure of merit is ( ) 2 112 2 2 2 120 2 3 1 3 20 22 ref FM post 3 )(22 3 SNR SNR meritofFigure ffff Pk ffN A ffN PkA f cfc ++= \u2212\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.