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 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 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 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: