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Practice over 1000+ GATE-level questions from this topic!

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Q#1 Random Variable and Random Process GATE EC 2000 MSQ +2 marks -0 marks

Zero mean white Gaussian noise with a two-sided power spectral density of  is passed through an ideal low pass filter with a cut-off frequency of 2 KHz and a pass band gain of 1, to produce the noise output n(t).        

(a) Obtain the total power in n(t).

(b) Find the autocorrelation function  of the noise n(t) as a function of .

(c) Two noise samples are taken at times and . Find the spacing  so that the product  has the most negative expected value and obtain this most negative expected value.

(a) Total Power = 16 W

(b)

(c)  

(c)

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