A new aspect of transition between line and continuous spectrum and its relation to seismic in influence on structures

Abstract

We considered a new view on transition process from periodic to aperiodic signals, in time and spectral domains, pointing out how the concept of infinity is involved. It contributes to better understanding of the nature of both spectral descriptions, and conditions of their practical use, particularly in unusual cases. There we highlight the invariance in spectrum convergence by introducing some numerical parameters which exactly describe such process. Their behaviour is numerically examined to detail. Also, we considered the opposite transition, from aperiodic to periodic, to clarify the meaning of spectral line. To suggest applicability of our analysis we used an actual seismic signal. By extracting the most prominent waveform part, regarding influence on structures, we formed a periodic signal which line spectrum can clearly show possible resonance with vibrating tones of structures.