Spectrograms

Spectrograms are visual representations of how the frequency content of a signal evolves over time. They are widely used in audio processing to analyze speech, music, environmental sounds, and other time-varying signals. A spectrogram is typically produced by applying a short-time Fourier transform (STFT) to the signal: the signal is divided into overlapping frames, each frame is windowed and transformed to the frequency domain, and the magnitude (often squared to produce power) is plotted as color or grayscale with time on the x-axis and frequency on the y-axis.

Key parameters include the window function (for example Hann or Hamming), the window length (which sets frequency resolution), and the hop size (overlap between frames). Longer windows provide finer frequency resolution but poorer time resolution, while shorter windows do the opposite. Frequency scales can be linear or logarithmic, and perceptually weighted scales such as mel or Bark are also used in some analyses. The spectrogram is commonly computed using fast Fourier transform algorithms.

Interpretation focuses on patterns in the time-frequency plane. Horizontal patterns indicate steady tones, while vertical lines reflect harmonics. Broad bands suggest noise or transient energy. Formants in speech appear as dark bands, and the trace of the fundamental frequency relates to pitch. Cepstral features like MFCCs can be derived from the spectrogram for use in pattern recognition and classification.

Variations include the power spectrogram (squared magnitude), multi-taper spectrograms, constant-Q spectrograms, and wavelet-based spectrograms (scalograms). Each emphasizes different time-frequency characteristics.

Applications and limitations: spectrograms are widely used in speech recognition, music information retrieval, instrument identification, medical and seismic signal analysis, and radar. They involve trade-offs between time and frequency resolution and can be affected by windowing choices, leakage, noise, and sampling rate.