The ERBlet transform: An auditory-based time-frequency representation with perfect reconstruction

This paper describes a method for obtaining a perceptually motivated and perfectly invertible time-frequency representation of a sound signal. Based on frame theory and the recent non-stationary Gabor transform, a linear representation with resolution evolving across frequency is formulated and implemented as a non-uniform filterbank. To match the human auditory time-frequency resolution, the transform uses Gaussian windows equidistantly spaced on the psychoacoustic “ERB” frequency scale. Additionally, the transform features adaptable resolution and redundancy. Simulations showed that perfect reconstruction can be achieved using fast iterative methods and preconditioning even using one filter per ERB and a very low redundancy (1.08). Comparison with a linear gammatone filterbank showed that the ERBlet approximates well the auditory time-frequency resolution.