EC GATE 2007 - Online Test
Q1. If the semi-circular control D of radius 2 is as shown in the figure, then the
value of the integral 
is
is
Answer : Option A
Explaination / Solution:
Q2. A 5-point sequence x n is given as x - 3 = 1, x - = 1, x - 1 = , x = 5 and x 1 = 1. Let X(ei𝜔) denoted the discrete-time Fourier transform of x n.
The value of 
is
is
Answer : Option B
Explaination / Solution:
Q3. An input to a 6-level quantizer has the probability density function f(x) as shown
in the figure. Decision boundaries of the quantizer are chosen so as to maximize the
entropy of the quantizer output. It is given that 3 consecutive decision boundaries
are' −1'. '0 ' and '1'.
The values of a and b are
Answer : Option A
Explaination / Solution:
Area under the pdf curve must be unity
2a + 4a + 4b = 1
2a + 8b = 1.................................................(1)
For maximum entropy three region must by equivaprobable thus
2a = 4b = 4b...............................................(2)
From (1) and (2) we get
b = 1/12 and a = 1/6
