Quantifying filter bank decorrelating performance via matrix diagonality

An important number of signal processing applications require decomposing a discrete-time signal into decorrelated frequency channels. Several algorithms have been used for this purpose. One of the most popular is the DFT, which is known to be far from optimal due to the presence of overlap between adjacent channels. Filter banks are an interesting alternative as they can be designed for reduced frequency overlap, which results in an approximately tridiagonal autocorrelation matrix. In order to compare the decorrelating ability of different transforms, we propose simple but useful measures via autocorrelation matrix diagonality. We develop analytical expressions and numerical examples to show that our measures are equivalent for well decorrelated signals, and related to the well known Itakura–Saito distortion measure.