# Log-spectral distance

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.