On the correlation of the DWT coefficients

The discrete wavelet transform (DWT) can be considered as a nonuniform octave filter bank or as an orthonormal matrix transform. Although the correlations in the DWT domain are obtained readily from the original signal correlations in the latter perspective, the former is necessary as well in order to interpret the statistics. Although the DWT is generally known to decorrelate a correlated signal, it actually depends on the spectral shape of the original signal. The decorrelation property should be applied only to the DWT coefficients that do not come from subbands with significant deviations from flatness. In particular, this is illustrated using an AR (autoregressive) process with different pole locations.