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Spectrum analysis is often applied to signals comprised of sinusoids. Sinusoidal signals are particularly interesting, because they share properties with both deterministic and random signals. On the one hand, we can describe them in terms of a simple equation. On the other hand, they have infinite energy, so we often characterize them in terms of their average power, just as with random signals. This problem explores some theoretical issues in modeling sinusoidal signals from the point of view of random signals. We can consider sinusoidal signals as stationary random signals by assuming that the signal model is s[n] = A cos(ω0n + θ ) for -∞
(a) Show that the autocorrelation function for such a signal is
(b) Using Eq. (11.34), write the set of equations that is satisfied by the coefficients of a 2nd-order linear predictor for this signal.
(c) Solve the equations in (b) for the optimum predictor coefficients. Your answer should be a function of ω0.
(e) Use Eq. (11.37) to determine an expression for the minimum mean-squared prediction error. Your answer should confirm why random sinusoidal signals are called "predictable" and/or "deterministic."
Compute the mean and variance for each of the following activities: Activit y A B C D E F G H I J Optimisti c 5 3 18 9 8 1 45 12 7 22 Pessimisti c 10 21 32 11 8 10 95 15 11 80 Most Likely 7 15 25 10 8 6 60 13 9 60
Human-Machine systems defined as a combination of humans and equipment interacting to achieve some desired result. Types of human-machine systems are Manual systems, Mechanical systems, and automated systems. **Systems Components are The human, Th..
Plot the fraction of ferrite, austenite, and cementite in equilibrium alloy containing (a) 0.6% C (b) 0.8% C and (c) 1.2% C as a function of temperature (25 C to 1400 C). What is the percentage of pearlite (eutectoid) in the above three cases at ro..
Design a Heat Exchanger for the Following Duty: Reduced crude oil leaving a distillation unit with a flow rate of 3166.04 kL/d at 268 oC and is to be cooled to 243 oC by exchange with 62.8 kg/s pre-flashed crude oil coming from pre-flash unit at 206 ..
Determine the Probability that an Ahmed energy state is occupied by an election it the slide is above the Fermi level by KT.
Then find the voltage across the 50-Ω resistor and the total power supplied by the source
In Bertrand competition firms decide independently what prices to set to maximizetheir individual profits. Suppose that there are two firms in a market sellingthe same product. Let D(p) = 9 - p be the market demand and let c1 = 1 andc2 = 7 be firm 1 ..
A nutritional Calorie is equal to 1000 calories (thermochemical calories), which is equal to 4.184 kJ. How many 8-in-high steps must a 180-lb man climb to expend the 400 Cal from the piece of cake? See Exercise 20 for the formula for potential ene..
If a saturated solution of NaHCO3 at 60°C is cooled and comes to equilibrium at 30°C, what percentage of the dissolved salt crystallizes?
Calculate the molar fraction of the system in the vapor phase
An alternative process for converting benzene to cyclohexane also uses a supported noble metal catalyst, but carries out the reaction in the liquid phase, at a temperature of 160 °C and pressure of 100 bare, in a slurry reactor.
Plot of the Fermi distribution function at two different temperatures. Calculate the Fermi timction at 6.5 eV if EF=6 .25 eV and T=300 K. Repeat for T=950 K assuming that the Fermi energy does not change. Plot the energy dependence of the ele..
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