Periodicity Analysis Using Morlet Wavelet Transform

This document presents a Morlet wavelet transform implementation designed for periodicity analysis of long time series data. The program employs complex Morlet wavelets to perform multi-scale decomposition of temporal signals, enabling comprehensive examination of cyclic patterns. Through wavelet coefficient computation and time-frequency localization, the algorithm reveals periodic characteristics across different temporal scales. Implementation typically involves convolving the input signal with dilated and translated versions of the mother wavelet, generating a scalogram that visualizes spectral power distribution over time. Users simply need to input their time series data and execute the program to obtain detailed periodicity analysis results, including dominant frequencies and their temporal evolution. By identifying hidden periodic patterns through wavelet coherence analysis and phase relationships, this tool facilitates more accurate predictions and data-driven decisions. The Morlet wavelet transform's Gaussian windowing property ensures optimal time-frequency resolution, making this implementation particularly valuable for analyzing non-stationary long-term time series data common in climate studies, financial analysis, and signal processing applications.