The Theory of Advanced Spectral Analysis Methods
S. Adarsh, M. Janga Reddy · 2021
This chapter presents the theoretical descriptions of advanced spectral analysis methods such as wavelet transform and Hilbert Huang Transform (HHT). The mathematical principles behind discrete WT, continuous WT, wavelet coherence and cross wavelet transform are presented. HHT comprise a data adaptive decomposition phase and the Hilbert transform phase. The algorithms of univariate decomposition methods such as Empirical Mode Decomposition (EMD) and ensemble EMD (EMD), complete ensemble EMD with adaptive noise and multivariate extension of EMD (MEMD) used in the decomposition phase are presented. The theoretical background of normalization-direct quadrature (N-DQ) scheme and arbitrary order Hilbert spectral analysis used in the Hilbert transform phase are presented. Time Dependent Intrinsic Correlation (TDIC) analysis is a running correlation method developed from HHT. The novel hybrid frameworks proposed such as MEMD-TDIC, MEMD-data driven technique, MEMD-scaling theory approach are explained in detail. These tools can be used for teleconnection, simulation and development of design tools in hydrology.