Consider a constant random process, X (t) = A, where A is a random variable. Use Definition A discrete random process, X[n], is generated by repeated tosses of a coin. Let the occurrence of a head be denoted by 1 and that of a tail by - 1. A new discrete random process is generated by Y [2n] = X [n] for n = 0, ± 1, ± 2 … and Y[n] = X [n + 1] for n odd (either positive or negative). Find the autocorrelation function for Y[n] to calculate the PSD of X (t).
Answer to relevant Questions(a) Prove that the expression for the PSD of thermal noise in a resistor converges to the constant as No / 2 = ktk / 2 as f→0. (b) Assuming a temperature of 298ok, find the range of frequencies over which thermal noise ...Let Where all of the ωn are non- zero constants, the an are constants, and the θn are IID random variables, each uniformly distributed over [0, 2π]. (a) Determine the autocorrelation function of X (t). (b) Determine the ...A white Gaussian noise process, , is input to two filters with impulse responses, h1(t) and h2 (t) , as shown in the accompanying figure. The corresponding outputs are Y1 (t) and Y2 (t), respectively. (a) Derive an ...A certain LTI system has an input/ output relationship given by (a) Find the output autocorrelation, RYY (τ), in terms of the input autocorrelation, RXX (τ). (b) Find the output PSD, SYY (τ), in terms of the input PSD, ...For the high- pass RC network shown, let X (t) = A sin (ω ct + θ) + N (t), where is white, WSS, Gaussian noise and θ is a random variable uniformly distributed over [0, 2π]. Assuming zero initial conditions: (a) Find ...
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