This　article　presents　the　theoretical　relationship　between　the　site　amplification　ratio　of　the　input　energy　spectrum　for　a　single-degree-of-freedom　system　(SDOF)　and　that　of　the　Fourier　amplitude　spectrum　(FAS).　The　relationship　indicates　that　the　input　energy　spectral　ratio　is　the　result　of　smoothing　the　square　of　the　Fourier　amplitude　spectral　ratio.　The　spectral　window　for　smoothing　is　determined　by　the　bedrock-motion　FAS　and　the　oscillator　transfer　function　for　the　relative　velocity.　The　characteristics　of　the　input　energy　spectral　ratio　were　derived　based　on　the　idea　of　smoothing　and　confirmed　based　on　real　seismic　records.　The　findings　of　this　study　contribute　to　a　better　understanding　of　site　effects　on　the　input　energy　spectrum.　©　Seismological　Society　of　America.