Tidsfrekvens

Tidsfrekvens, or time-frequency analysis, refers to a family of methods for analyzing signals whose spectral content changes over time. These representations aim to describe a signal with both time and frequency coordinates, enabling the study of non-stationary phenomena such as speech, music, and biomedical signals.

A widely used approach is the short-time Fourier transform (STFT). The signal is multiplied by a window that localizes it in time, and a Fourier transform is computed within each window, producing a spectrogram. The choice of window length controls the trade-off between time resolution and frequency resolution.

Other techniques include wavelet transforms, which decompose a signal into time-scale representations, producing scalograms. Quadratic time-frequency distributions, such as the Wigner-Ville distribution, offer higher resolution but can create cross-term interferences that complicate interpretation. Reassignment methods and ridge detection are used to sharpen representations.

Applications cover audio and speech analysis, music information retrieval, radar and sonar, seismology, and biomedical signals like EEG and ECG. The field also addresses practical issues such as noise robustness, stationarity assumptions, and computational cost.

Historically, tidsfrekvens analysis emerged from the development of the windowed Fourier transform by Dennis Gabor in the 1940s and was extended in various directions by researchers such as Ville, Cohen, and Mallat. Today, time-frequency representations are implemented in many signal-processing toolkits and are a standard part of modern analysis.