Logspectrograms

Logspectrograms are a type of spectrogram that represents the spectral content of an audio signal on a logarithmic scale for the magnitude, typically using a decibel (dB) scale. They are commonly produced by first computing the short-time Fourier transform (STFT) of the signal, taking the magnitude (or power) spectrum, and then applying a logarithm. Formally, if X(t, f) is the STFT, a log-spectrogram may be defined as S_log(t, f) = 20 log10(|X(t, f)|) in dB or equivalently 10 log10(|X(t, f)|^2). A small floor is often added to avoid log(0).

Computation details commonly involve a windowed analysis: choosing a window function (such as Hann), a window length, and a hop size to produce overlapping frames. The resulting S_log emphasizes quieter components and reduces the dominance of very loud portions, producing a representation that better aligns with human loudness perception in many contexts.

Applications and use cases include visualization of complex audio content, and as input features for machine learning tasks in speech recognition, speaker identification, and music information retrieval. Log scaling helps stabilize variance and can improve performance of classifiers and neural networks by compressing dynamic range and highlighting relevant patterns.

Relation to related representations: a log-spectrogram refers to the log-scaled magnitude or power spectrum on a linear frequency axis. A log-mel spectrogram is a common variant that first applies mel filter banks to produce mel energies and then takes the logarithm. Logspectrograms are widely used as a general-purpose audio representation, with choices about flooring, reference level, and STFT parameters influencing detail and interpretability.