Let 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) has a line spectrum and write the PSD X (t) of in terms of the Fourier Series coefficients of the periodic signal S (t).
Answer to relevant QuestionsA sinusoidal signal of the form X (t) = bcos (2πft + θ), is transmitted from a fixed platform. The signal is received by an antenna which is on a mobile platform that is in motion relative to the transmitter, with a ...Consider a random process Z (t) = X (t) + Y (t). (a) Find an expression for SZZ (f) in terms of SXX (f), SYY (f) and SXY (f). (b) Under what conditions does SZZ (f) = SXX (f) + SYY (f)? Suppose we use an AR (2) model to predict the next value of a random process based on observations of the two most recent samples. That is, we form Ẏ [n + 1] = a1Y [n] + a2Y [n – 1] (a) Derive an expression for the mean- ...(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 ...A white noise process, X (t), with a PSD of SXX (f) = No / 2 is passed through a finite time integrator whose output is given by Find the following: (a) The PSD of the output process, (b) The total power in the output ...
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