Unit Impulse Function
Unit Impulse Function The above figure shows a function which has a zero value when t is negative , rises instantaneously to a value 1/t₀ when 0<t<t₀ , and is zero thereafter. If we let t₀--> 0 , this function tends towards infinity as t₀--> 0, but width decreases inversely with the magnitude ; hence area under the curve remains finite . The unit impulse function is represented by δ(t) . Among Physicists, the unit impulse function is referred to as the 'Dirac δ-function ' after the name of great Physicist Dirac , who is the first to use this function in systematic manner . The Dirac δ - function at the point t=a as in above figure is represented by δ(t-a) . Thus {0 for t < a δ(t-a) ={ 1/t₀ for a<t<a+t₀ {0 for t> a+t₀ .......(1) Where t₀ --> 0 in the limit . The Laplace transform of δ(t-a) is