A 1-MHz carrier is frequency-modulated by a single tone of frequency 2 kHz, resulting in the peak frequency deviation of10 kHz. a.What is the bandwidth occupied by the modulated signal?Plot the spectrum of the FM signal (only side bands in the Carson's bandwidth).F b. If the amplitude of the modulating sinusoidal signal is increased by a factor of 3 and its frequency is decreased to1 kHz, how is the bandwidth of the modulated signal modified? Plot the spectrum of the FM signal. c. Repeat part (b) with the frequency of the modulating sinu-soidal signal increased to 3 kHz.

P-2.18 Determine the values of the parameters {o, q,A} in the equations below. \text { (b) } 10 \cos (9 \mathrm{t}-\pi / 3)=\mathrm{A} \cos (\omega \mathrm{t}-\pi / 2)+5 \cos (\omega \mathrm{t}+\varphi)

P-3.1 A signal x(t) has the two-sided spectrum representation shown in Fig. P-3.1 (see below). (a) Write an equation for x(t) as a sum of cosines.

P-2.2 Figure P-2.2 (see below) is a plot of a sinusoidal wave. From the plot, determine values for the amplitude(A), phase (p), and frequency (coo) needed in the representation: x(t) = Acos(oot + p)Give the answer as numerical values, including the units where applicable.

How many photons are arriving per second at a receiver if the power is 1 nW at wave-length 1.3 um?

Suppose a fiber system operates at a wavelength of 1.55 um. The system can handle digital information at a data rate equal to one-hundredth of one percent of the optical frequency.How many HDTV compressed video channels can be multiplexed onto this fiber system?

Consider an FM signal generated by modulating a 10-MHz car-rier by a 1-kHz sinusoidal waveform such that peak frequency deviation is 2.5 kHz. a. Determine the bandwidth of the modulated signal. b. If the modulating signal amplitude is doubled, determine the bandwidth of the modulated signal. c. Determine the bandwidth of the modulated signal if the modulating signal frequency is doubled. 1. Determine the bandwidth of the modulated signal if both the-amplitude and frequency of the modulating signal are doubled.

1.4 A receiver requires 10 nW as input power. If all the system losses add up to 50 dB, then how much power is required from the source?

Let the modulating signal be Write an expression for the FM waveform XFM(t) whenAc = 100, fc = 5 MHz, and k = 200 Hz/V. Determine maximum frequency deviation deltafmax, maximum phase deviation Aphi max, and deviation ratio D of the modulated signal. Determine the bandwidth of the modulated signal.

A particular radar receiver has a noise figure of 2.1 dB when operating from anantenna with an effective noise temperature Ta = 180 K. What is the standardnoise figure of the receiver?

Give the answers in both Cartesian form (x + jy) and polar form (reje).

-5 For a two-stage amplifier Te1 = 360 K and Te2 510 K. When operatingwith a source for which T, = 200 K, the noise figure is known to be 3.82(or 5.820 dB). What is the available power gain of the first stage?-

11. What is a universal gate? Please justify your reasoning and give an example. 12. Implement the following Product-of-Sums function using logic gates. F = (X+Y)(Y+Z) 13. For the given function in question 12, implement F as a Sum-of-Products using logic gates. 14. Implement a 4-bit parallel adder using full adders. Clearly label the bits of the inputs. 15. Consider the question 14. If the carry propagation delay for a full adder is 2ns, how fast can the inputs to the 4-bit parallel adder be updated? 16. You are given a task of designing a circuit to produce a repetitive sequence of 1,2,3,1,2,3,... Represent this problem in a state diagram. 17. Consider the question 16. Derive the state table. 18. Consider the question 16 and 17. Draw the circuit diagram for the circuit. 19. Assume that you have access to a clock signal at a frequency of f. Propose a circuit that generates another clock signal with a frequency of f/4. 20. What is the difference between combinational and sequential logic circuits.

P-3.2 A signal composed of sinusoids is given by the equation x(t)=10 \cos (800 \pi t+\pi / 4)+7 \cos (1200 \pi t-\pi / 3)-3 \cos (1600 \pi t) (a) Sketch the spectrum of this signal, indicating the complex amplitude of each frequency component. Make separate plots for real/imaginary or magnitude/phase of the complex amplitudes at each frequency.

8 Work Problem 4.4-6 except for a noise figure and noise temperature of 3.5 dB and 80 K, respectively.