Establish fan-out and performance for broader painless NSGTs

Establish the fan-out and performance of the exact factorisation when applied to painless nonstationary Gabor transforms beyond the evaluated constant-Q transform configuration, including auditory filterbanks.

Background

The factorisation is stated to apply beyond the evaluated constant-Q transform to other painless nonstationary Gabor transforms, such as auditory filterbanks. The paper notes that the relevant fan-out and computational performance have not yet been established for these broader transform families, leaving their efficiency and implementation characteristics unresolved.

References

The construction also applies to other painless \acp{nsgt} beyond the CQT configuration evaluated in this paper, such as auditory filterbanks, although their fan-out and performance remain to be established.

— Exact Factorisation and Fast Computation of Invertible Constant-Q Transforms  (2609.29119 - Franchino et al., 24 Sep 2026) in Section 6, “Conclusion”