Våglettransformasjoner

Våglettransformasjoner, or wavelet transforms, are mathematical tools used to decompose a signal into different frequency components, much like a Fourier transform. However, unlike the Fourier transform which uses sine and cosine waves of infinite extent, wavelet transforms utilize short, wave-like functions called wavelets. These wavelets are localized in both time and frequency, allowing for a more detailed analysis of signals that change over time.

The core idea behind a wavelet transform is to represent a signal as a sum of scaled and translated versions of a mother wavelet. By varying the scale, we can analyze different frequency bands, and by translating the wavelet, we can pinpoint the time at which these frequencies occur. This time-frequency localization is a key advantage of wavelet transforms for analyzing non-stationary signals, such as audio, images, or financial data.

There are two main types of wavelet transforms: the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). The CWT provides a continuous representation of the signal in the time-frequency plane, while the DWT offers a discrete, often more efficient, representation that is widely used in signal compression and denoising applications. Wavelet transforms have found applications in numerous fields, including signal processing, image compression (like JPEG2000), data analysis, and even in areas like quantum mechanics and geophysics.