# Perceptual importance of KLT eigenchannels

The Karhunen-Leve Transform (KLT) can be used to reduce the interchannel
redundancy of multichannel audio signals due to its mathematical properties as
KLT can transform a set of correlated signals into a set of uncorrelated
signals (Yang, 2003). In addition to signal decorrelation,
KLT has another very valuable property: the KL-transformed signals are ordered
hierarchically according to the amount of signal variance they explain. However,
it cannot be directly deduced that the mathematical character of KLT will lead
to the same effect on people's perception of the quality of multichannel audio.
The perceptual importance of Karhunen- Leve transformed multichannel audio
signals was systematically studied using listening tests. Three eigenvalue
extraction methods were employed as follows: a covariance matrix based
eigenvalue extraction (Cov-KLT), a correlation matrix based eigenvalue
extraction (Corr-KLT) and a perceptually optimised eigenvalue extraction method
(PO-KLT). Conclusions can be summarised as follows:

1. Basic audio quality decreased as the number of removed eigenchannels
increased.

2. KLT eigenchannel removal caused less degradation in audio quality for
multichannel audio with high interchannel correlation than for those items with
low interchannel correlation.

3. Three eigenvalue extraction methods resulted in similar performance of
BAQ for FF and FF+C recordings. But for FB and FB+C recordings, the KLT
processing based on covariance matrix (Cov-KLT) and perceptually optimised
covariance matrix (PO-KLT) caused smaller audio quality degradation than that
caused by the KLT processing based on correlation matrix (Corr-KLT).

4. In general, for Corr-KLT and Cov-KLT, the orders of perceptual importance
(PI) and statistical importance (SI) of eigenchannels are the same, whereas for
the PO-KLT, the perceptual importance of the 2 nd eigenchannel is higher than
the 1 st eigenchannel (see Figure 1). However, it is difficult to generalise
these observations as the results strongly depend on programme material.

*Figure 1: Comparison between Perceptual Importance (PI) and Statistical Importance (SI) of eigenchannels *

This work is reported in detail in [P2].