STFTspektrogram

An STFT spectrogram, or short-time Fourier transform spectrogram, is a time–frequency representation of a signal produced by applying the short-time Fourier transform across successive windows of the signal and plotting the squared magnitude or magnitude of the results as a function of time and frequency. The continuous form X(τ, ω) is the Fourier transform of the windowed signal x(t)w(t−τ). In discrete-time signals, X[m, k] = Σ_n x[n] w[n−m] e^{−j 2π k n / N}, where w is a window function and m indexes time frames, k frequency bins.

Interpretation and use: The spectrogram shows how spectral content evolves over time, revealing transients, harmonics, and tonal changes. Window length and overlap control time and frequency resolution: longer windows give finer frequency resolution but poorer time resolution, shorter windows do the opposite. Common window choices include Hann, Hamming, and Blackman; overlaps typically 50% or more are used to ensure continuity. The spectrogram is often displayed as the squared magnitude |X[m,k]|^2 or the log magnitude, sometimes converted to decibels, to emphasize weaker components.

Applications and limitations: Applications include speech and music analysis, speaker recognition, audio scene analysis, and biomedical signals. Limitations include the fixed resolution for all frequencies and potential leakage. Alternatives or enhancements include multi-resolution approaches (e.g., wavelets), constant-Q spectrograms, and reassignment methods; cepstral representations such as mel spectrograms are widely used in audio processing. The STFT spectrogram remains a foundational visualization and feature representation in signal processing.