AES E-Library

Towards an Inverse Constant Q Transform

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.

Authors: Cranitch, Matt; Cychowski, Marcin T.; FitzGerald, Derry
Affiliation: Cork Institute of Technology
AES Convention:120 (May 2006) Paper Number:6671 Import into BibTeX
Session Subject:Analysis and Synthesis of Sound; Mobile Phone Audio; Automobile Audio

Click to purchase paper or login as an AES member. If your company or school subscribes to the E-Library then switch to the institutional version. If you are not an AES member and would like to subscribe to the E-Library then Join the AES!

This paper costs $20 for non-members, $5 for AES members and is free for E-Library subscribers.

Learn more about the AES E-Library

E-Library Location: (CD 120Papers)   /120/6671.pdf

Start a discussion about this paper!