The subject of this thesis focuses on the study, analysis, and current challenges of recently introduced methods for flow field analysis and decomposition, namely Spectral Proper Orthogonal Decomposition (SPOD) and Wavelet Transform (WT). Spectral POD is a decomposition technique designed to identify energy-ranked modes within a flow field, where each mode corresponds to a specific frequency, allowing for the distinctive separation of phenomena occurring at different frequencies and energy levels. Wavelet transform is another powerful method for analysing signals in both time and frequency domains, by decomposing a signal into different scales with the use of wavelet functions, it provides a localized representation of signal features, making it suitable for detecting transient events or localized variations, like identifying coherent structures and turbulence study.