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We analyse the power spectral density (PSD) $S_T(f)$ (with $T$ being theobservation time and $f$ is the frequency) of a fractional Brownian motion(fBm), with an arbitrary Hurst index $H \in (0,1)$, undergoing a stochasticresetting to the origin at a constant rate $r$ - the resetting processintroduced some time ago as an example of an efficient, optimisable searchalgorithm. To this end, we first derive an exact expression for the covariancefunction of an arbitrary (not necessarily a fBm) process with a reset,expressing it through the covariance function of the parental process without areset, which yields the desired result for the fBm in a particular case. Wethen use this result to compute exactly the power spectral density for fBM forall frequency $f$. The asymptotic, large frequency $f$ behaviour of the PSDturns out to be distinctly different for sub- $(H < 1/2)$ and super-diffusive$(H > 1/2)$ fBms. We show that for large $f$, the PSD has a power law tail:$S_T(f) \sim 1/f^{\gamma}$ where the exponent $\gamma= 2H+1$ for $0<H\le 1/2$(sub-diffusive fBm), while $\gamma= 2$ for all $1/2\le H<1$. Thus, somewhatunexpectedly, the exponent $\gamma=2$ in the superdiffusive case $H>1/2$ sticksto its Brownian value and does not depend on $H$.

Spectral content of fractional Brownian motion with stochastic reset