Question: Show that the estimator for the autocorrelation function XX
Show that the estimator for the autocorrelation function, ṘXX (τ), described in Equation (10.26) is unbiased. That is, show that E [ṘXX (τ)] = RXX (τ).
Answer to relevant QuestionsSuppose is a zero- mean, WSS, Gaussian random process. Find an expression for the variance of the estimate of the autocorrelation function, ṘXX (t). That is, find Var (ṘXX (t)). (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 ...Find the PSD for a process for which RXX (τ) = 1 t for all τ. A discrete random sequence is the input to a discrete linear filter h [n]. The output is Y [n]. Let Z [n] = X [n+ i] – Y [n]. Find E [Z2 [n]], in terms of the autocorrelation functions for X [n] and Y [n].and the cross- ...Suppose you want to learn the characteristics of a certain filter. A white noise source with an amplitude of 15 watts/ Hz is connected to the input of the filter. The power spectrum of the filter output is measured and found ...
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