Morwavelets

Morwavelets are a type of wavelet function that are particularly well-suited for analyzing and representing signals with non-stationary characteristics. They are named after their developer, Jean-Michel Morlet. Morwavelets are defined by a Gaussian window, which allows for good localization in both time and frequency. This property makes them effective in identifying and analyzing transient events or sudden changes within a signal.

The mathematical formulation of a morwavelet involves a complex exponential function modulated by a Gaussian envelope. This structure enables the morwavelet transform to decompose a signal into its constituent frequencies and observe how these frequencies evolve over time. Unlike some other wavelets, morwavelets are continuous, meaning the transform is applied using an integral rather than a summation. This continuity can offer a more detailed representation of the signal.

Applications of morwavelets are found in various fields. In geophysics, they are used for seismic data analysis to detect fault lines and underground structures. In image processing, morwavelets can be employed for edge detection and texture analysis. They are also utilized in speech recognition and biomedical signal processing, such as the analysis of electroencephalogram (EEG) or electrocardiogram (ECG) data. The ability of morwavelets to capture localized temporal and spectral information makes them a versatile tool for understanding complex signals.