Våglettransformen

The Våglettransformen, often translated as the wavelet transform, is a mathematical tool used to decompose a signal into different frequency components. Unlike the Fourier transform, which analyzes a signal in terms of its constituent frequencies over its entire duration, the wavelet transform provides both frequency and time localization. This means it can tell you not only what frequencies are present in a signal but also when they occur.

The core idea behind the wavelet transform involves using small, oscillating functions called wavelets. These wavelets are scaled and translated to match different parts of the signal. A larger wavelet corresponds to lower frequencies and a longer time duration, while a smaller wavelet corresponds to higher frequencies and a shorter time duration. By correlating the signal with these wavelets, the transform reveals the energy or amplitude of specific frequency components at specific points in time.

There are various types of wavelet transforms, including the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). The CWT provides a detailed time-frequency representation, while the DWT offers a more compressed representation, often used for signal compression and denoising.

The Våglettransformen has found widespread applications in fields such as image and audio compression, signal denoising, pattern recognition, medical imaging, and financial time series analysis. Its ability to capture both transient and oscillatory features in data makes it a powerful technique for analyzing complex signals.