A frequency domain approach to some results on fractional Brownian motion

Let $X$ be a fractional Brownian motion. It is known that $M_t=int m_t dX,, tge 0$, where $m_t$ is a certain kernel, defines a martingale $M$, and also that $X$ can be represented by $X_t=int x_t dM,, tge 0$, for some kernel $x_t$. We derive these results by using the spectral representation of the covariance function of $X$. A formula for the covariance between $X$ and $M$ is also given.