Conclusion
During this lecture we introduce the spectral analysis techniques which is widely used in environmental and engineering field. The PSD is the Fourier transform of the auto-correlation function. We showed that the spectral analysis finds applications in many diverse fields. In vibration monitoring,the spectral content of measured signals give information on the wear and other characteristics of mechanical parts under study. In economics, meteorology, astronomy and several other fields, the spectral analysis may reveal “hidden periodicities” in the studied data, which are to be associated with cyclic behavior or recurring processes. We highlight also the scale invariance propriety which can be observed using the spectral analysis, this propriety is very important when we characterize the field using multifractal analysis. Note that the PSD give information about the second order statistics of the studied field, in order to go beyond this order we will perform the multifractal analysis which will be described in the next lecture.
