  In 1918 S. Ramanujan defined a family of trigonometric sum now known as
Ramanujan sums. In the last few years, Ramanujan sums have inspired the signal
processing community. In this paper, we have defined an operator termed here as
Ramanujan operator. In this paper it has been proved that these operator
possesses properties of first derivative and second derivative with a
particular shift. Generalised multiplicative property and new method of
computing Ramanujan sums are also derived in terms of interpolation.
