# itakura.dist: Itakuro-Saito distance In seewave: Sound Analysis and Synthesis

## Description

Compare two distributions (e.g. two frequency spectra) by computing the Itakuro-Saito distance

## Usage

 1 itakura.dist(spec1, spec2, scale=FALSE)

## Arguments

 spec1 any distribution, especially a spectrum obtained with spec or meanspec (not in dB). This can be either a two-column matrix (col1 = frequency, col2 = amplitude) or a vector (amplitude). spec2 any distribution, especially a spectrum obtained with spec or meanspec (not in dB). This can be either a two-column matrix (col1 = frequency, col2 = amplitude) or a vector (amplitude). scale a logical, if TRUE the distance is scaled by dividing the distance by the length of spec1 (or spec2).

## Details

The Itakura-Saito (I-S) distance is a non-symmetric measure of the difference between two probability distributions. It is here adapted for frequency spectra. The distance is asymmetric, ie computing the I-S distance between spec1 and spec2 is not the same as computing it between spec2 and spec1. A symmetry can be obtained by calculating the mean between the two directions.
The distance is obtained following:

D(spec1 || spec2) = sum(spec1/spec2 - log(spec1/spec2) - 1)

## Value

The function returns a list of three items:

 D1 The I-S distance of 'spec2' with respect to 'spec1' (i.e. D(spec1 || spec2)) D2 The I-S distance of 'spec1' with respect to 'spec2' (i.e. D(spec2 || spec1)) D The symmetric distance (i.e. D = 0.5*(D1+D2))

If scale = TRUE the distance is divided by the length of spec1 (or spec2).

## Note

The function works for both Hz and (htk-)mel scales.

## Author(s)

Jerome Sueur, improved by Laurent Lellouch