waveletfunksjon

Wavelet functions are a class of mathematical functions used in wavelet analysis, a technique for analyzing and representing signals or functions. Unlike traditional Fourier analysis, which uses sine and cosine functions, wavelet analysis uses wavelets, which are localized in both time and frequency domains. This localization allows for a more detailed analysis of signals, particularly those with non-stationary characteristics.

Wavelet functions are typically defined as a family of functions generated from a single prototype wavelet, known as the mother wavelet, through translations and dilations. The continuous wavelet transform (CWT) is a mathematical operation that decomposes a signal into wavelets, providing a time-frequency representation of the signal. The discrete wavelet transform (DWT), on the other hand, is a sampled version of the CWT, making it computationally efficient and suitable for digital signal processing applications.

Wavelet functions have found applications in various fields, including signal processing, image compression, and data analysis. They are particularly useful for analyzing signals with transient features, such as those encountered in audio processing, seismic data analysis, and medical signal analysis. The choice of wavelet function depends on the specific application and the characteristics of the signal being analyzed. Commonly used wavelet functions include the Haar wavelet, the Daubechies wavelets, and the Morlet wavelet.