The Fourier transform, response spectra and their relationship through the statistics of oscillator response

The concept of the Damped Fourier Transform (D. F. S.) has been developed through an understanding of the nature of the response of a damped oscillator to input ground accelerations. It has been shown that such a transform serves as a lower bound to the corresponding damped velocity spectrum curves. A review of the statistics of the maxima of a random function has been done and its application to the determination of response spectrum estimates has been studied. Such simple statistical estimates have been found to be very useful in improving our physical understanding of response spectra.