logspectrogram

A log-spectrogram is a representation of sound or other time-varying signals that displays the logarithm of the magnitude of the spectrogram. A spectrogram itself is a visual representation of the spectrum of frequencies of a signal as it varies with time. It is typically generated by taking the short-time Fourier transform (STFT) of a signal, which breaks the signal into short, overlapping segments and computes the frequency content of each segment.

The process of creating a log-spectrogram involves first computing the standard spectrogram. This results in a matrix where one axis represents time, the other represents frequency, and the values within the matrix represent the magnitude (or power) of the signal at that specific time and frequency. The next step is to apply a logarithmic transformation to these magnitude values. This is often done using the decibel scale, where the magnitude is converted to 20 times the base-10 logarithm of the ratio of the magnitude to a reference magnitude, or similarly for power using 10 times the logarithm.

The reason for using a logarithmic scale is that human perception of sound intensity is logarithmic, not linear. This means that a doubling of sound pressure does not sound twice as loud. By using a log-spectrogram, the visual representation better aligns with how humans perceive loudness, making it easier to distinguish between quiet and loud sounds. Additionally, the logarithmic scale compresses the dynamic range of the signal, allowing quieter details to be more visible alongside louder components without being completely masked. This makes log-spectrograms particularly useful in audio analysis, speech recognition, and music information retrieval.