Aikataajuusmenetelmät

Aikataajuusmenetelmät, often translated as time-frequency analysis methods, are a class of signal processing techniques used to analyze signals that vary in time, such as audio, vibration, or biomedical signals. Unlike traditional Fourier analysis, which decomposes a signal into its constituent frequencies over its entire duration, time-frequency methods provide information about how the frequency content of a signal changes over time. This is crucial for understanding non-stationary signals where the frequency components are not constant.

Several time-frequency analysis methods exist, each with its own strengths and weaknesses. The Short-Time Fourier Transform (STFT) is a fundamental technique that divides the signal into short, overlapping segments and applies a Fourier Transform to each segment. This offers a trade-off between time and frequency resolution: a shorter window provides better time resolution but poorer frequency resolution, and vice versa.

More advanced methods include the Wigner-Ville distribution, which offers higher resolution than the STFT but suffers from cross-term artifacts, especially for multi-component signals. Wavelet transforms represent another significant category, using basis functions called wavelets that are localized in both time and frequency. Different types of wavelets can be chosen to match the characteristics of the signal being analyzed, offering adaptive time-frequency resolution. Other notable methods include the Hilbert-Huang Transform (HHT), which decomposes signals into intrinsic mode functions (IMFs) and then performs empirical mode decomposition and Hilbert spectral analysis.

Time-frequency analysis is widely applied in fields such as speech processing, radar and sonar, seismic data analysis, and the study of biological signals like electroencephalograms (EEGs) and electrocardiograms (ECGs). These methods are essential for identifying transient events, tracking frequency modulations, and revealing hidden patterns in complex signals.