waveletelemzés

Wavelet analysis is a mathematical tool used to decompose a signal into different frequency components, much like Fourier analysis. However, unlike Fourier analysis, which uses sines and cosines of infinite duration, wavelet analysis employs short, wave-like functions called wavelets. These wavelets are localized in both time and frequency, meaning they can capture transient features and changes in a signal that might be missed by traditional Fourier methods.

The core idea is to use a "mother wavelet" and scale and shift it to create a family of wavelets. These wavelets are then used to analyze the signal. The decomposition process yields coefficients that represent the signal's similarity to each wavelet at a particular scale and time. This information can then be used for various applications, including signal denoising, compression, feature extraction, and pattern recognition.

Wavelet analysis is particularly effective for non-stationary signals, which are signals whose statistical properties change over time. Examples include audio signals, seismic data, and financial time series. The ability of wavelets to provide both time and frequency localization makes them ideal for analyzing such signals. Different types of wavelets exist, each with its own mathematical properties and suitability for specific tasks. The choice of wavelet can significantly impact the results of the analysis.