Phase derivative correction of bandwidth-extended signals for perceptual audio codecs

Bandwidth extension methods, such as spectral band replication (SBR), are often used in low-bit-rate codecs. They allow transmitting only a relatively narrow low-frequency region alongside with parametric information about the higher bands. The signal for the higher bands is obtained by simply copying it from the transmitted low-frequency region. The copied-up signal is processed by multiplying the magnitude spectrum with suitable gains based on the transmitted parameters to obtain a similar magnitude spectrum as that of the original signal. However, the phase spectrum of the copied-up signal is typically not processed, but is directly used. In this paper, we describe what are the perceptual consequences of using directly the copied-up phase spectrum. Based on the observed effects, two metrics for detecting the perceptually most significant effects are proposed. Based on these, methods how to correct the phase spectrum are proposed, as well as strategies for minimizing the amount of transmitted additional parameter values for performing the correction. Finally, the results of formal listening tests are presented.