Non-constant Q Multi-Resolution Transforms: Properties, Applications, and Fast Algorithm

摘要

The constant-Q based wavelet transform is the most effective means of quantitatively characterizing high fre- quency transient signals. The study developed a novel non constant-Q based multi-resolution transform (NCQM) and pro- vides a precision analysis descriptor for both low and high fre- quency transients. The properties of this novel NCQM kernel are thoroughly examined and then the striking conceptual resem- blance, energy conservation characteristic, and power spectrum close forms are derived. The rapid algorithm of NCQM is also presented and its excellent performance in noisy environments is demonstrated.