This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the “Damped Fourier Spectrum” (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial conditions. The D.F.S. represents a new way of “smoothing” the classical Fourier Transform by using a physically based filter.