Tidfrekvensopløsning

Tidfrekvensopløsning refers to the ability to simultaneously determine both the time and frequency at which a signal occurs. In signal processing, this is a fundamental concept with significant implications for analyzing non-stationary signals, which are signals whose frequency content changes over time.

When analyzing a signal, one might be interested in "what frequencies are present" and "when are they present." A standard Fourier Transform provides excellent frequency resolution but sacrifices time resolution, essentially giving an average frequency content over the entire signal duration. Conversely, a short-time Fourier Transform (STFT) divides the signal into short segments, analyzes each segment for its frequency content, and thus offers better time resolution than a full Fourier Transform. However, there is an inherent trade-off: improving time resolution in an STFT necessitates a shorter analysis window, which in turn reduces frequency resolution, and vice versa. This is a manifestation of the Heisenberg uncertainty principle applied to signal analysis.

The choice of time-frequency resolution depends heavily on the application. For analyzing rapidly changing transient events, high time resolution is crucial. For identifying distinct harmonic components that persist for longer durations, high frequency resolution might be more important. Various time-frequency representations, such as wavelets, aim to provide a more flexible resolution trade-off than the fixed window of the STFT.