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The Itakura–Saito distance is a measure of the perceptual difference between an original spectrum $P(\omega )$ and an approximation $\hat{P}(\omega )$ of that spectrum. It was proposed by Fumitada Itakura and Shuzo Saito in the 1970s while they were with NTT.

The distance is defined as:

$D_{IS}(P(\omega ),\hat{P}(\omega ))=\frac{1}{2\pi }\underset{-\pi }{\overset{\pi }{\int }}[\frac{P(\omega )}{\hat{P}(\omega )}-\log \frac{P(\omega )}{\hat{P}(\omega )}-1]d\omega$

The Itakura–Saito distance is a Bregman divergence, but is not a true metric since it is not symmetric.

See also

• Log-spectral distance

References

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