A continuous-time signal x(t) is defined as :

\(x(\mathrm{t})=\left\{\begin{array}{cc} 5 & -2 \leq \mathrm{t} \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\)

The energy of signal x(t) is :

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NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper

Answer 1

Concept:

The energy of a continuous-time signal x(t) is given by: \( E = \int_{-\infty}^{\infty} |x(t)|^2 dt \)

Given:

\( x(t) = \begin{cases} 5, & -2 \leq t \leq 2 \\ 0, & \text{otherwise} \end{cases} \)

Calculation:

Since \( x(t) = 5 \) from \( t = -2 \) to \( t = 2 \), we compute the energy as:

\( E = \int_{-2}^{2} |5|^2 dt = \int_{-2}^{2} 25 \, dt = 25 \times (2 - (-2)) = 25 \times 4 = 100 \)