Latest Gate Aptitude Question SOLUTION: If x(n) ={n for 0<=n<=10 0, otherwise y(n)= x(n) * x(n) then y(4)=?

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(#M40033087) GATE Numerical Ability question signals Keep an EYE

If x(n) ={n for 0<=n<=10
0, otherwise
y(n)= x(n) * x(n)
then y(4)=?

Asked In Gate D Venkat Rami Reddy (10 years ago)

Unsolved Read Solution (10)

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RAKESH  (10 years ago)

y(n)= x(n) * x(n)
y(4)= x(4) * x(4)

now, x(n) ={n for n belongs[0,10] so, x(4)= 4 as
so, y(4)= 4*4 =16

Is this solution Helpfull? Yes (2) | No (2)  

D Venkat Rami Reddy  (10 years ago)

given is finite sample sequence starting from 0.
total num of samples 11 including x(0)=0.
so linear convolution is
0000000000...
0123456789...
02468..............
039.................
048............
y(n)={0,0,1,4,10,23,...............}
ds seq start from 0 sample
y(0)=0
y(1)=0
............y(4)=10

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Vivek Jain  (10 years ago)

16? that simple? Gate? or am i missing something?

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RAKESH  (10 years ago)

y(n)= x(n) * x(n)
y(4)= x(4) * x(4)

now, x(n) ={n for 0

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Sridhar Reddy  (10 years ago)

hey its 20 u can do it simple by using periodic convolution.

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Sridhar Reddy  (10 years ago)

sorry linear convolution not periodic

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D Venkat Rami Reddy  (10 years ago)

guys it is convolution not multiplication
I hope ans is 10 by linear convolution

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Soniya Sharma  (10 years ago)

simple , 4*4= 16 it is

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Sridhar Reddy  (10 years ago)

1 2 3 4 . . .
1 2 3 4 . . .
_______________. . . .
1 2 3 4.....
2 4 6 8.....
3 6 9.....
4 8....
_________________
1 4 10 20 .....

=> y(4)=20

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virendra dubey  (10 years ago)

x(n)=n...here n=4..so x(4)=4
y(n)=x(n)*x(n)
y(4)=x(4)*x(4)=4*4=16

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