Consider a random sinusoidal process of the form X (t) = bcos (2πft + θ), where θ has an arbitrary PDF fθ(θ), . Analytically determine how the PSD of X (t) depends on fθ(θ). Give an intuitive explanation for your result.
Answer to relevant QuestionsLet be a deterministic periodic waveform with period to. A random process is constructed according to X (t) = s (t – T) Where T is a random variable uniformly distributed over [0, to]. Show that the random process X (t) ...Let X (t) be a random process whose PSD is shown in the accompanying figure. A new process is formed by multiplying by a carrier to produce X (t), Y (t) = X (t) cos( ωot + θ) Where θ is uniform over [0, 2π] and ...Consider an AR (2) process which is described by the recursion Y [n] = a1Y [n– 1] + a2Y [n– 2] + X [n] Where is an IID random process with zero- mean and variance σ2X. (a) Show that the autocorrelation function of the ...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 ...Suppose X (t) is a stationary zero- mean Gaussian random process with PSD, SXX (f). (a) Find Y (t) = X2 (t) the PSD of in terms of SXX (f). (b) Sketch the resulting PSD if SXX (f) = rect (f /2B). (c) Is WSS?
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