An upper bound on the quality of artificial bandwidth extension of narrowband speech signals

The aim of the artificial bandwidth extension (BWE) of speech signals is to recover wideband speech from bandlimited speech. As the BWE algorithm is supposed to operate without additional side information on the original wideband speech, it has to exploit mutual dependencies between the available and missing frequency bands of the speech signal. In this paper the BWE is examined from an information theoretic perspective. After defining a performance measure, and introducing a few assumptions on a generalized BWE algorithm, a general relationship between mutual information and the maximum achievable estimation performance is formulated, which ensues an upper bound on the performance of BWE algorithms. Finally, some measurements considering a representative BWE scenario are presented.