Towards an Inverse Constant Q Transform

Cranitch M, Cychowski MT, FitzGerald D. Towards an Inverse Constant Q Transform. In: AES Convention 120. Audio Engineering Society; 2006. Paper 6671. Available from: https://aes.org/publications/elibrary-page/?id=13475

@inproceedings{Cranitch2006_13475,
  author = {Cranitch, Matt and Cychowski, Marcin T. and FitzGerald, Derry},
  title = {{Towards an Inverse Constant Q Transform}},
  booktitle = {AES Convention 120},
  note = {Paper 6671},
  year = {2006},
  month = may,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=13475}
}

TY  - CPAPER
TI  - Towards an Inverse Constant Q Transform
AU  - Cranitch, Matt
AU  - Cychowski, Marcin T.
AU  - FitzGerald, Derry
T2  - AES Convention 120
M1  - Paper 6671
PY  - 2006
DA  - 2006/05/06
UR  - https://aes.org/publications/elibrary-page/?id=13475
PB  - Audio Engineering Society
LA  - en
AB  - The Constant Q transform has found use in the analysis of musical signals due to its logarithmic frequency resolution. Unfortunately, a considerable drawback of the Constant Q transform is that there is no inverse transform. Here we show it is possible to obtain a good quality approximate inverse to the Constant Q transform provided that the signal to be inverted has a sparse representation in the Discrete Fourier Transform domain. This inverse is obtained through the use of `0 and `1 minimisation approaches to project the signal from the constant Q domain back to the Discrete Fourier Transform domain. Once the signal has been projected back to the Discrete Fourier Transform domain, the signal can be recovered by performing an inverse Discrete Fourier Transform.
ER  -