Langtidsspektralanalyse

Langtidsspektralanalyse refers to methods for estimating and interpreting the spectral content of signals over long time spans. It addresses non-stationarity by recognizing that the frequency content may drift slowly over time, so the spectrum is allowed to change across the observation period.

Practically, it often involves segmenting the data into blocks that are treated as approximately stationary, computing spectra for each block, and either averaging to obtain a stable long-term spectrum or tracking changes with time-frequency representations such as the multi-taper spectrum, windowed Fourier transforms with long windows, or wavelet-based approaches. Bayesian and state-space methods can model the spectrum as a slowly varying process.

Typical goals include identifying persistent oscillations (cycles), distinguishing long-period signals from noise, and quantifying how spectral power distributes across frequencies over the observation period. Common data issues include irregular sampling, gaps, trends, and seasonal effects which must be removed or modeled.

Applications span geophysics and climatology (decadal climate modes, solar activity), oceanography (wave-energy spectra), economics (business cycles), astronomy (long-baseline pulsation analysis), and engineering (structural monitoring). Limitations include the need for long records, sensitivity to windowing choices, and a trade-off between frequency resolution and temporal resolution. The field sits at the intersection of classical spectral analysis and time-frequency methods.