Short-time Fourier transform & spectrogram

The short-time Fourier transform slides a fixed-length window along the signal and computes the Fourier transform within each window, producing a two-dimensional map of frequency content over time. The squared magnitude of that map is the spectrogram. Because the window length is constant, the STFT imposes a uniform time-frequency resolution across all frequencies, a rectangular tiling of the plane.

This uniformity is both its strength (a simple, interpretable, linear representation) and its limitation: a window short enough to catch fast gamma transients is too short to resolve slow theta structure, and vice versa. In BCI the STFT and spectrogram are common for visualizing event-related spectral changes such as ERD/ERS, but for signals spanning several octaves the wavelet transform's frequency-dependent windows are usually preferred.