The Dirac delta function (t) is defined as

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The Dirac delta function δ(t) is defined as

A. \[\delta \left( t \right) = \left\{ \begin{array}{l} 1\,\,\,\,t = 0\\ 0\,\,\,\,{\rm{otherwise}} \end{array} \right.\]

B. \[\delta \left( t \right) = \left\{ \begin{array}{l} \infty \,\,\,\,t = 0\\ 0\,\,\,\,{\rm{otherwise}} \end{array} \right.\]

C. \[\delta \left( t \right) = \left\{ \begin{array}{l} 1\,\,\,\,t = 0\\ 0\,\,\,\,{\rm{otherwise}} \end{array} \right.{\rm{ and }}\int\limits_{ - \infty }^\infty {\delta \left( t \right)dt = 1} \]

D. \[\delta \left( t \right) = \left\{ \begin{array}{l} \infty \,\,\,\,t = 0\\ 0\,\,\,\,{\rm{otherwise}} \end{array} \right.{\rm{ and }}\int\limits_{ - \infty }^\infty {\delta \left( t \right)dt = 1} \]

Answer: Option D

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The Dirac delta function (t) is defined as

The Dirac delta function δ(t) is defined as

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