Relative attenuation by a linear filter ($\eta =|H({\omega }_n)|/|H({\omega }_s)|$)

For a linear time-invariant system, a sinusoidal wanted signal at ${\omega }_s$ and an unwanted sinusoidal component at ${\omega }_n$ acquire their separate frequency response factors. The ratio of their output amplitudes, divided by their input amplitude ratio, is $\eta =|H({\omega }_n)|/|H({\omega }_s)|$. An amplitude attenuation factor of $F=1/\eta$ corresponds to a factor $F^2$ in squared-amplitude power ratios under a common impedance convention. The unwanted component's own absolute attenuation is $|H({\omega }_n)|$, which need not equal its attenuation relative to the wanted signal.