University of Akron Department of Electrical and Computer Engineering 4400 341: Introduction to Communication Systems - Spring 2015 Assignment – 3 3.8-4 Find the mean square value (or power) of the output voltage y(t) of the system shown in Figure 1 if the input voltage PSD �! � = Π(��). Calculate the power (mean square value) of the input signal x(t). Figure 1 Solution: 4.2-1 You are given the baseband signals: I. � � = cos(1000��) II. � � = 2cos 1000�� + sin(2000��) III. � � = cos(1000��) cos(3000��) IV. exp (−10 � ) For each one, do the following: a) Sketch the spectrum of m(t) b) Sketch the spectrum of the DSB-SC signal m(t)cos(10,000��) c) Identify the upper sideband (USB) and lower sideband (LSB) spectra. Solution: 4.2-8 The system shown in Figure 2 is used for scrambling audio signals. The output y(t) is the scrambled version of the input m(t). a) Find the spectrum of the scrambled signal y(t) b) Suggest a method of descrambling y(t) to obtain m(t) Figure 2 Solution: 4.3-1 In an amplitude modulation system, the message signal is given by Figure 3 and the carrier frequency is 1 kHz. The modulator output is: �!" � = 2[� + 0.5� � ] cos(�!�) a) Determine the average message power. b) If b = 1, determine the modulation index and the modulation power efficiency. c) Sketch the modulated signal of part (a) in the time domain. d) If b = 0.5, repeat parts (a) and (b) Figure 3 Solution: 4.3-5 In a DSB-SC amplitude modulation system, the message signal is � � = �!!!�(� − 2) and the carrier signal is cos(2000��). a) Find and sketch the Fourier transform of the message signal. b) Find and sketch the Fourier transform of the modulated signal. Solution: 4.3-8 In the early days of radio, AM signals were demodulated by a crystal detector followed by a low-pass filter and a dc blocker, as shown in Figure 4. Assume a crystal detector to be basically a squaring device. Determine the signals at point a,b,c and d. Point out the distortion term in the output y(t). Show that if � ≫ �(�) , the distortion is small. Figure 4 Solution: .