A quasi-orthogonal, invertible, and perceptually relevant time-frequency transform for audio coding

We describe ERB-MDCT, an invertible real-valued time-frequency transform based on MDCT, which is widely used in audio coding (e.g. MP3 and AAC). ERB-MDCT was designed similarly to ERBLet, a recent invertible transform with a resolution evolving across frequency to match the perceptual ERB frequency scale, while the frequency scale in most invertible transforms (e.g. MDCT) is uniform. ERB-MDCT has mostly the same frequency scale as ERBLet, but the main improvement is that atoms are quasi-orthogonal, i.e. its redundancy is close to 1. Furthermore, the energy is more sparse in the time-frequency plane. Thus, it is more suitable for audio coding than ERBLet.