Consider a very simple model for the amplitude of an acoustic signal as it propagates away from a source. The real amplitude A at distance d (in meters) is defined as A(d) = Aolejkd| where A0 = 2.5 and k = -j0.25. Which of the plots below shows A(d)? ☐ LO 5 4 3 U 5 1 4 3 2 2 1 0 T 0 0.5 1 1.5 2 2.5 3 d M wwwww 0.5 1 1.5 2 2.5 3 d U ☐ 5 4 3 2 1 0 0 0.5 1 1.5 50 2 2.5 3 5 4 3 2 1 0 0 0.5 1 1.5 2 2.5 3

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Ope X. The frequency spectrum of an AM signal is shown below: 5.5V 1V 1V 52kHz 58kHz a) if the modulating signal is a sine wave, write the equation of the modulating signal b) if the carrier signal is a cosine wave, write the equation of the carrier signal c) calculate the current of the AM signal flowing through a 300-ohm load

XY=54

Plot two cycles of a 25 Hz sine signal, starting at time zero, labeling the time axis at all peaks and crossings of the time axis. Write an equation describing the signal of Double Side Band Amplitude Modulated with a carrier frequency of 250 Hz.

1.) A carrier with an RMS voltage of 2V and a frequency of 1.5 MHz is modulated by a sine wave with a frequency of 500 Hz and amplitude of 1 Vrms. Write the equation for the resulting signal in its basic and extended form. 2.) A certain transmitter radiates 9 kW with the carrier unmodulated, and 10.125 kW when the carrier is sinusoidally modulated. If another sine wave corresponding to 40% modulation, is transmitted simultaneously, determine the total radiated power.

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A sequence of alternating 1s and 0s is transmitted as a square wave. What is the fundamentalfrequency and how many harmonics can be used if the available BW is 100 MHz and a data rate of 56Mbps is desired? Express the signal as a mathematical function of time (s(t)) and sketch the resultingsignal in both the time and frequency domains. Is this a “good enough” representation of the squarewave? Why or why not?

Q7. A sinusoid wave of frequency vm = 10 kHz is used to frequency modulate a carrier wave of frequency vc = 96 MHz with a a peak frequency deviation Ay = 24 kHz. (a) Does this modulation correspond to narrowband or wideband FM? (b) Using the plots of Bessel functions in figure Q7 and the recursive relation for Bessel functions of the first kind, 2n Jn-1(B) + Jp+1 (B) = (6) or otherwise, determine the relative amplitude of the the carrier and the significant sidebands. (c) Sketch the power spectrum of this FM waveform. (d) State Carson's rule for determining the number of significant sidebands. (e) What is the maximum bandwidth given by Carson's rule for this modulated waveform? (f) Compare the bandwidth of your calculated power spectrum in part (c) with the maxi- mum bandwidth given by Carson's rule. (g) What is the equivalent AM modulation index obtained if this signal is demodulated with a high-pass RC filter discriminator? 1.0 Jo(x) 0.8 J1 (x) - 0.6 0.4 - 0.2 0.0 5/ 7 8 () -0.2 1 3…

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