Discrete vs Continuous Time Impulse Signals

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reddvoid
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Whats the difference between a discrete time impulse and a continuous time impulse signal ?
 
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DT: the function is zero for all points not equal to 0 and equals 1 at 0
CT: the function is zero for all points not equal to 0, equals infinity at 1, but the total area under the impulse is 1