GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 63 of 65

Marks: +1, -0

Consider the two continuous-time signals defined below:
These signals are sampled with a sampling period of

T=0.25

seconds to obtain discrete-time signals

x_{1}[n]

and

x_{2}[n]

, respectively. Which one of the following statements is true?

Solution:

x_{1}(t)=\{\table {|t|}\text ",",-1 ≤ t ≤ 1 ; 0\text ","\text ",", \;\text " otherwise."

T_{s}=

sampling time-period

=0.25 {sec}

x_{1}(n)=\{1,0.75,0.5,0.25,0,0.25,0.5,0.75,1\}

Now,

x_{2}(t)=\{ \table1-{|t|}\text ",",-1≤t≤1;0\text ",",\otherwise

x_{2}(n)=\{0,0.25,0.5,0.75,1,0.75,0.5,0.25,0\}

Since

x_{1}(n)

is having one more non-zero sample of amplitude ' 1 ' as compared to

x_{2}(n)

. Therefore, energy of

x_{1}(n)

is greater than energy of

x_{2}(n)

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