ABSTRACT

A Hierarchical Constant Q Transform for Partial Tracking in Musical Signals

A hierarchical constant Q transform for spectral analysis of monophonic musical signals is given. The proposed hierarchical constant Q transform provides a method for improvement of time resolution at lower frequencies with reduced computational costs. The transform is a multi-level Q implementation that starts with a low Q and progressively increases the Q up to the desired maximum value. Initially, the lowest level (lowest Q) is calculated for all bins of the transform. Then, Q and the number of bins are doubled at each level, making the frequency bin spacing half that of the previous level. Calculation of bins at each higher level is conditional to the output of the transform at a previous level. In this way only those bins that have significant response are calculated thus reducing the number of calculations. The advantages brought about by the hierarchical constant-Q transform are two-fold: first reduced time smearing of the analized signal at lower frequencies is achieved and second the computation time is significantly reduced compared to a complete transform with the same frequency resolution.