tidsfrekvensrepræsentation

A time-frequency representation is a mathematical tool used to display how the frequency content of a signal changes over time. Unlike a simple frequency spectrum, which shows the overall frequencies present in a signal but not when they occur, a time-frequency representation provides a two-dimensional plot where one axis represents time and the other represents frequency. The intensity or color at any point on this plot indicates the magnitude of a particular frequency at a particular moment.

This type of representation is particularly useful for analyzing non-stationary signals, which are signals whose frequency content changes over time. Examples of such signals include speech, music, seismic waves, and radar signals. By observing a time-frequency representation, one can identify transient events, track frequency modulations, and understand the dynamic spectral behavior of a signal.

Several methods exist for generating time-frequency representations, each with its own trade-offs between time and frequency resolution. Common techniques include the Short-Time Fourier Transform (STFT), the Wigner-Ville distribution, and wavelet transforms. The STFT divides the signal into short, overlapping segments and computes the Fourier transform for each segment, providing a compromise between time and frequency localization. Wavelet transforms offer a more adaptable resolution, providing better frequency resolution at low frequencies and better time resolution at high frequencies. The choice of representation depends on the specific characteristics of the signal and the analysis goals.