vågletstransformen

The vågletstransformen, often translated as the wavelet transform, is a mathematical tool used to analyze signals or data by breaking them down into different frequency components at different resolutions. Unlike the Fourier transform, which analyzes a signal in terms of pure sine and cosine waves of infinite duration, the wavelet transform uses wavelets – small, oscillating functions that are localized in both time and frequency.

This localization is a key advantage. It allows the wavelet transform to capture transient features, sudden changes, and localized events within a signal that might be missed by the Fourier transform. The transform essentially provides a time-frequency representation of the signal, showing how the frequency content changes over time.

The process involves convolving the signal with a scaled and translated version of a chosen wavelet function. Different scales correspond to different frequencies, with larger scales representing lower frequencies and smaller scales representing higher frequencies. Translation shifts the wavelet along the signal, allowing for analysis at different points in time.

The vågletstransformen has found widespread applications in various fields, including image compression (like JPEG2000), signal processing, audio analysis, pattern recognition, and the analysis of seismic data. It is particularly useful for analyzing non-stationary signals, where the frequency content varies over time. The choice of the specific wavelet function depends on the nature of the signal and the desired analysis.