Squared error as a measure of phase distortion

In this article, we investigate how accurately the squared error captures perceptual errors introduced by Fourier phase spectrum changes. We measure the perceptual error using the Auditory Image Model by Patterson et al.. The squared error is found to represent the perceptual error well for low squared errors but it saturates. Thus, a further increase in squared error does on average not lead to any further increase in perceptual error. This suggests that encoding phase using squared-error trained codebooks only improves perceived quality when operating at high bit rates. To verify this, phase was encoded with codebooks of different sizes. As expected, increasing the codebook size has very little influence on the average perceptual error for low rates, which is confirmed by listening tests. Our results suggest that a direct phase codebook is an inefficient representation of the relevant information contained in phase.