Introduction
The Ramanujan Sums were first proposed by Srinivasan Ramanujan in 1918, and have become exceedingly popular in the fields of signal processing,time-frequency analysis and shape recognition. The sums are by nature, orthogonal. This results in them offering excellent conservation of energy, which is a property shared by Fourier Transform as well.
We have used Matrix Multiplication to obtain the Ramanujan Basis, for our computation. The Ramanujan Sums are defined as nth powers of qthprimitive roots of unity, which can be computed using this simple formula:
Where
The Ramanujan matrix can be defined as:
The 2-D forward Ramanujan Sum Transform is given as:
which in matrix terms can be defined as
and the inverse 2D Ramanujan transform in matrix terms is:
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