Log-spectral distance

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The log-spectral distance (LSD), also referred to as log-spectral distortion, is a distance measure (expressed in dB) between two spectra. The log-spectral distance between spectra $P\left(\omega \right)$ and ${\hat {P}}\left(\omega \right)$ is defined as:

$D_{{LS}}={\sqrt {{\frac {1}{2\pi }}\int _{{-\pi }}^{\pi }\left[10\log _{{10}}{\frac {P(\omega )}{{\hat {P}}(\omega )}}\right]^{2}\,d\omega }},$

where $P\left(\omega \right)$ and ${\hat {P}}\left(\omega \right)$ are power spectra. Unlike the Itakura–Saito distance, the log-spectral distance is symmetric.

Log-spectral distance

See also