1
GATE ECE 2022
+1
-0.33

The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.

Statement I : The system is necessarily a pure delay system for inputs which are bandlimited to $$-$$$$\alpha$$ $$\le$$ f $$\le$$ $$\alpha$$.

Statement II : For any wide-sense stationary input process with power spectral density SX(f), the output power spectral density SY(f) obeys SY(f) = SX(f) for $$-$$$$\alpha$$ $$\le$$ f $$\le$$ $$\alpha$$.

Which one of the following combinations is true?

A
Statement I is correct, Statement II is correct
B
Statement I is correct, Statement II is incorrect
C
Statement I is incorrect, Statement II is correct
D
Statement I is incorrect, Statement II is incorrect
2
GATE ECE 2022
Numerical
+1
-0.33

Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), as shown in the figure.

Consider a 1 bit quantizer that maps positive samples to value $$\alpha$$ and others to value $$\beta$$. If $$\alpha$$* and $$\beta$$* are the respective choices for $$\alpha$$ and $$\beta$$ that minimize the mean square quantization error, then ($$\alpha$$* $$-$$ $$\beta$$*) = ___________ (rounded off to two decimal places).

3
GATE ECE 2017 Set 2
Numerical
+1
-0
Consider the random process
x(t) = U + Vt.
Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is _________________
4
GATE ECE 2014 Set 4
+1
-0.3
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be
A
Poisson
B
Gaussian
C
Exponential
D
Gamma
EXAM MAP
Medical
NEET