GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 64 of 65

Marks: +1, -0

The signal energy of the continuous-time signal

x(t)=[(t-1) u(t-1)]-[(t-2) u(t-2)]-[(t-3) u(t-3)]+[(t-4) u(t-4)]

Solution:

From the given equation graph of 𝑥(𝑡) will be

E\{x(t)\}=∫↙{-∞}↖{∞}{|x(t)|}^{2} d t

=∫↙{1}↖{2}(t-1)^{2} d t+∫↙{2}↖{3} 1^{2} d t+∫↙{3}↖{4}-(t+4)^{2} d t

=\;{1}/{3}+1+\;{1}/{3}=\;{5}/{3}

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