KurzzeitFourierTransformation

Kurzzeit-Fourier-Transformation (KZFT), in English the Short-Time Fourier Transform (STFT), is a signal-processing method for analyzing non-stationary signals. It computes the Fourier transform on successive, windowed portions of a signal, producing a two-dimensional time–frequency representation often displayed as a spectrogram.

The process uses a window function that slides along the signal. Within each window, the spectrum is computed, yielding the temporal evolution of frequency content. Window length trades off time versus frequency resolution: longer windows improve frequency detail but blur timing; shorter windows do the opposite.

Common windows include Hann, Hamming, Blackman, and Gaussian. The Gaussian window is central to the Gabor transform, a close relative of the STFT with optimal time–frequency concentration.

Applications span speech and music analysis, telecommunications, radar, and biomedical signals. The STFT is well suited for tracking transients and evolving spectra, but the fixed window imposes a uniform resolution over time and can cause spectral leakage at segment boundaries. Extensions address these issues with adaptive windowing, multi-taper approaches, and reassignment methods.

Historically, the concept emerged in the mid-20th century, with Dennis Gabor contributing foundational ideas on time–frequency representations. The term Short-Time Fourier Transform became standard in subsequent decades, and the technique remains a fundamental tool in both research and applied signal processing.

Related topics include the Fourier transform, spectrograms, and time-frequency analysis.