Combination methods

Time-frequency representations (TFRs) such as the short-time Fourier transform (STFT) or the constant-Q transform (CQT) can be computed with different resolutions. Notably, achieving a high frequency resolution requires long analysis windows, which in turn leads to a poor time resolution. Conversely, a high time resolution can be obtained with short windows, but at the expense of a poor frequency resolution. This tradeoff is a known challenge in signal processing and music information retrieval.

This package provides several methods that attempt to address this tradeoff by combining multiple TFRs (computed with different resolutions) into a single representation that preserves the best aspects of each individual TFR, achieving good localization in both time and frequency. We refer to these techniques as combination methods. If you are interested in learning more about combination methods, we recommend the following reading material:

• Package release article: To be added.

• D.Sc. thesis on combination methods: M. do V. M. da Costa, Novel time-frequency representations for music information retrieval, D.Sc., Federal University of Rio de Janeiro, Rio de Janeiro, Brasil (2020 Apr.).

The methods provided in this package are listed below. While we don’t provide a detailed explanation of each method here, each section provides the information necessary to use the method with ctfr as well as additional references for further reading.

• Simple binwise methods
• Sample-weighted geometric mean
• Lukin-Todd
• Smoothed local sparsity
• Fast local sparsity