Spectrogram

A spectrogram is a visual representation of the spectrum of a signal as it varies over time. For audio or other time-varying signals, it shows how the frequency content changes, with the intensity indicating amplitude or power.

Construction typically uses a short-time Fourier transform (STFT). The signal is divided into overlapping frames, each windowed by a function such as a Hann or Hamming window. The Fourier transform of each windowed frame yields a frequency spectrum, and the magnitudes (often converted to power or decibels) are plotted as a color or grayscale value. The horizontal axis represents time, the vertical axis frequency, and the color encodes the spectral magnitude. Some spectrograms use linear frequency scales, others use logarithmic or perceptual scales.

Variants and interpretations: Mel spectrograms map frequencies to a perceptual mel scale to emphasize pitch perception, while narrow-band spectrograms reveal fine temporal detail and wide-band spectrograms highlight harmonic structure. Wavelet-based time-frequency representations offer alternative decompositions. Limitations arise from the time-frequency trade-off dictated by windowing, potential artifacts from window choice, and sensitivity to noise.

Applications: Spectrograms are widely used in speech analysis, music information retrieval, linguistics, and bioacoustics. They assist in tasks such as phoneme identification, pitch tracking, instrument recognition, and acoustic event detection, as well as in engineering fields like sonar, radar, and structural health monitoring.