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Prashant kumar Best Answer
Dirac delta function has the unit of the inverse of its argument. Now you can ask me if Dirac delta is a function then why it has unit since functions are unitless. But Dirac delta function is not a function at all. it is a distribution. Or we can say it is generalised function. If x in meter the delta(x) is in meter inverse. then what would be the unit of delta(x-1). also has unit of meter inverse. Actual thing is if x is in meter then only meter is add or subtract to this therefore it is actually written as delta(x-1m).