  An arithmetical function $f$ is said to be even (mod r) if f(n)=f((n,r)) for
all n\in\Z^+, where (n, r) is the greatest common divisor of n and r. We adopt
a linear algebraic approach to show that the Discrete Fourier Transform of an
even function (mod r) can be written in terms of Ramanujan's sum and may thus
be referred to as the Discrete Ramanujan-Fourier Transform.
