nsider an ideal low-pass filtered white noise process, n(t), whose auto-correlation function T) and power spectral density (PSD) SN(f) are depicted in the figure below. --8 28 la) (b) (a) Power spectral density. (b) Autocorrelation function etermine the average power of the noise process n(t). Determine a suitable value for the constant A.

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a) Consider an ideal low-pass filtered white noise process, n(t), whose auto-correlation function
RN(T) and power spectral density (PSD) SN(f) are depicted in the figure below.
Syin
Ry(r)
A
-B
B
(a)
(h)
(a) Power spectral density. (b) Autocorrelation function
i) Determine the average power of the noise process n(t).
ii) Determine a suitable value for the constant A.
b) The output of an oscillator is described by
Y(t)=Acos(wt)+B,
where A-N(0,2), B-N(2,3), A and B are independent, and w=0.10 t.
i) Find the mean of Y(t).
ii) Determine the autocorrelation function of Y(t).
Transcribed Image Text:a) Consider an ideal low-pass filtered white noise process, n(t), whose auto-correlation function RN(T) and power spectral density (PSD) SN(f) are depicted in the figure below. Syin Ry(r) A -B B (a) (h) (a) Power spectral density. (b) Autocorrelation function i) Determine the average power of the noise process n(t). ii) Determine a suitable value for the constant A. b) The output of an oscillator is described by Y(t)=Acos(wt)+B, where A-N(0,2), B-N(2,3), A and B are independent, and w=0.10 t. i) Find the mean of Y(t). ii) Determine the autocorrelation function of Y(t).
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