Literature Overview
This section provides references and resources for wavelet coherence, time-frequency analysis, and related signal processing methods.
Wavelet-Based Time-Frequency Fingerprinting for Feature Extraction of Traditional Irish Music
This work presents a wavelet-based approach to time-frequency fingerprinting for time series feature extraction, with a focus on audio identification from live recordings of traditional Irish tunes. The challenges of identifying features in time-series data are addressed by employing a continuous wavelet transform to extract spectral features and wavelet coherence analysis is used to compare recorded audio spectrograms to synthetically generated tunes. The synthetic tunes are derived from ABC notation, which is a common symbolic representation for Irish music. Experimental results demonstrate that the wavelet-based method can accurately and efficiently identify recorded tunes. This research study also details the performance of the wavelet coherence model, highlighting its strengths over other methods of time-frequency decomposition. Additionally, we discuss and deploy the model on several applications beyond music, including in EEG signal analysis and financial time series forecasting.
The Coherix project is a continuation of the methods explored in this thesis, which focuses on advanced wavelet coherence techniques for Irish tune identification.
Interdecadal Changes in the ENSO-Monsoon System
This seminal paper introduces the concept of wavelet coherence as a localized correlation coefficient in time-frequency space. Torrence and Webster developed this method to track chaotic interactions in monsoon systems influenced by El Niño over multiple decades, enabling the identification of regions in time-frequency space where two time series co-vary.
The El Niño–Southern Oscillation (ENSO) and Indian monsoon are shown to have undergone significant interdecadal changes in variance and coherency over the last 125 years. Wavelet analysis is applied to indexes of equatorial Pacific sea surface temperature (Niño3 SST), the Southern Oscillation index, and all-India rainfall. Time series of 2–7-yr variance indicate intervals of high ENSO–monsoon variance (1875–1920 and 1960–90) and an interval of low variance (1920–60). The ENSO–monsoon variance also contains a modulation of ENSO–monsoon amplitudes on a 12–20-yr timescale.
The annual-cycle (1 yr) variance time series of Niño3 SST and Indian rainfall is negatively correlated with the interannual ENSO signal. The 1-yr variance is larger during 1935–60, suggesting a negative correlation between annual-cycle variance and ENSO variance on interdecadal timescales.
The method of wavelet coherency is applied to the ENSO and monsoon indexes. The Niño3 SST and Indian rainfall are found to be highly coherent, especially during intervals of high variance. The Niño3 SST and Indian rainfall are approximately 180° out of phase and show a gradual increase in phase difference versus Fourier period. All of the results are shown to be robust with respect to different datasets and analysis methods.
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View Paper →Financial Signal Processing
An introduction to wavelets and other filtering methods in finance, covering practical applications of wavelet analysis in financial time series.
This comprehensive book covers the application of wavelet transforms to financial data analysis, including denoising, feature extraction, and risk management applications.
Reference book - Available through academic publishers
View Book →Fast Continuous Wavelet Transform
The fast continuous wavelet transformation (fCWT) enables real-time, high-quality, and noise-resistant time–frequency analysis. This method is described in the following Nature Computational Science article.