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**Q1:**2.25 Consider a time-shifted set of orthonormal rectangular pulses with amplitudes given by s(0) = +0.0460-0.0460j s(8)= +0.0460 -0.0460j s(1) = -0.1320-0.0020js(9)= +0.0020 +0.1320j s(2) = -0.0130 +0.0790j s(10) = -0.0790 +0.0130j s(3) = +0.1430 +0.0130j s(11) = -0.0130 -0.1430j s(4) = +0.0920 + 0.0000j s(12) = +0.0000 - 0.0920j s(5) = +0.1430+ 0.0130j s(13)= -0.0130 - 0.1430j s(6) = -0.0130 +0.0790j s(14)= -0.0790+ 0.0130j s(7) = -0.1320-0.0020j s(15)= +0.0020 +0.1320j. The signal is then 15 s(t) = s(n)pr (t-nT). #0 This signal is used in the preamble of the IEEE 802.11 system. The signal is filtered with a filter with impulse response h(t) s*(16T-1). = (a) Find and plot the magnitude of the output of the filter. (b) If the signal is repeated eight times, plot the real part, imaginary part, and magnitude of the output of the same filter.See Answer**Q2:**5. Communication System Parameters [12 points] Consider the following communication system with constellation with 16 points in 16 dimensions as given in Question 1.5 (second set) of Chapter 1 of the textbook. The modulation is with the orthonormal waveforms given by (t)= Po(t-nT), for n=1,2,3,..., 15, and po(t) is the squarcroot raised cosine pulse with T = 0.0001 and a=0.5. Find the following parameters of the system: • Energy per bit Es • Rate R • Power P, Bandwidth W. The second set is attached below./nA second signal set with M = 16 signals in 16 dimensions that can transmit 4 bits of information has the following signals: So = A(+1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1) $₁ = A(+1,-1, +1, −1, +1, −1, +1, −1, +1, −1, +1, −1, +1,-1, +1, -1) $₂ = A(+1, +1,-1, −1, +1, +1, −1, −1, +1, +1, − 1, −1, +1, +1,-1,-1) $3 = A(+1,-1,-1, +1, +1, −1, −1, +1, +1, −1, −1, +1, +1,-1,-1, +1) $4 = A(+1, +1, +1, +1, −1, −1, −1, −1, +1, +1, +1, +1, −1, −1, −1, −1) $5 = A(+1,-1, +1, −1, −1, +1, −1, +1, +1, −1, +1, −1, −1, +1, −1, +1) S6 = A(+1, +1,-1, −1, −1, −1, +1, +1, +1, +1, −1, −1, −1, −1, +1, +1) $7 = A(+1,-1,-1, +1, −1, +1, +1, −1, +1, −1, −1, +1, −1, +1, +1, −1) $g = A(+1, +1, +1, +1, +1, +1, +1, +1, −1, −1, −1, -1,-1,-1,-1,-1) $9 = A(+1,-1, +1, −1, +1, −1, +1, −1, −1, +1, −1, +1,-1, +1,-1, +1) S10 = A(+1, +1,−1, −1, +1, +1, −1, −1, −1, −1, +1, +1, −1, −1, +1, +1) S11 = A(+1,-1, −1, +1, +1, −1, −1, +1, −1, +1, +1, −1, −1, +1, +1, -1) $12 = A(+1, +1, +1, +1, −1, −1, −1, −1, −1, −1, −1, −1, +1, +1, +1, +1) S13 = A(+1,-1, +1, −1, −1, +1, −1, +1, −1, +1, −1, +1, +1, −1, +1, -1) S14 = A(+1, +1,−1, −1, −1, −1, +1, +1, −1, −1, +1, +1, +1, +1, −1, −1) S15 = A(+1,-1,-1, +1, −1, +1, +1, −1, −1, +1, +1, −1, +1, −1, −1, +1)See Answer**Q3:**3.1 Let X be a random variable with density function £x(x) = { 8** x 20 x < 0. (a) Let y = + √x (positive square-root). Find the density function, fy(y), of y for all values of y. (b) Let Z = ax + b where a is a positive constant. Find the density function, fz(2), for all values of Z.See Answer**Q4:**1. (a) What is the equation for the received signal power at a monostatic radar in terms of: Pt transmit power, Gt= Gr=G antenna gain, o RCS, R range to target, f frequency, Ltot total losses? (b) What are the types of losses comprising Ltot? (c) How is receiver noise related to noise figure and other parameters? (d) If (S/N)min is the minimum detectable SNR, find the relationship between & and antenna gain when other parameters are held constant: o = g(G:other parameters)See Answer**Q5:**1.8 Estimate how many light pulses can be transmitted per second by a manually operated blinker-light system. What do you conclude about the information capacity of this manual system and how it compares with the capacity of modern fiber optic telephone links?See Answer

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