waveletdekomposioon

Wavelet decomposition is a mathematical technique used to break down a signal or function into different frequency components. Unlike the Fourier transform, which represents a signal as a sum of sine and cosine waves of infinite duration, wavelet decomposition uses wavelets, which are short, localized oscillations. This localization in both time and frequency allows for a more detailed analysis of signals that may have transient features or varying frequency content over time.

The process involves applying a series of filters to the signal. High-pass filters capture high-frequency details, while low-pass filters capture the overall trend or approximation of the signal. This decomposition can be performed recursively, breaking down the low-frequency approximation into further levels of detail and approximation. Each level of decomposition provides a set of coefficients that represent the signal at a particular scale and location.

Wavelet decomposition has found applications in various fields. In image processing, it's used for compression, denoising, and feature extraction. In signal processing, it aids in analyzing non-stationary signals like audio or seismic data. It's also utilized in areas such as medical imaging, financial analysis, and pattern recognition. The ability to analyze signals at multiple resolutions makes wavelet decomposition a powerful tool for understanding complex data.