Problem 9.9 A sample function )()2cos()( twtfAtx cc += \u3c0 is applied to a low-pass RC filter. The amplitude Ac and frequency fc of the sinusoidal component are constant, and w(t) is white noise of zero mean and power spectral density N0/2. Find an expression for the output signal-to-noise ratio with the sinusoidal component of x(t) regarded as the signal of interest. Solution The noise variance is proportional to the noise bandwidth of the filter so from Example 8.16, ( )[ ] 002 4 1 NRCNBtn N ==E and the signal power is fir a sinusoid, so the signal-to-noise ratio is given by 2/2cA 0 2 0 2 2 4 2 N RCA RC N ASNR cc = \u239f\u23a0 \u239e\u239c\u239d \u239b= 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.