On the mutual information between frequency bands in speech

In this paper we investigate the mutual information in speech between the spectral envelope of the high frequency band and low frequency bands of various widths. Direct methods on the computation of the mutual information often result in an excessive amount of data required even for modest situations. We reduce the required amount of data by quantizing the low band leading to a lower bound expression on the mutual information. We indicate by simulation that this lower bound is in the same order of magnitude as the true mutual information. Simulations on speech show that we have no less than 0.1 bit of shared information between the slope of the high band and the low frequency band from 0-4 kHz. Performing the analogous simulation with the gain of the high band we obtained no less than 0.45 bit of mutual information