Multiresolution Sinusoidal Modeling

Abstract

As indicated in the previous chapter, the standard sinusoidal model has difficulty modeling broadband processes — both noiselike components and timelocalized transient events such as attacks. Such broadband processes thus appear in the residual of the sinusoidal analysis-synthesis. A perceptual model for noiselike components will be presented in Chapter 4; that representation, however, is inadequate for time-localized events such as attack artifacts, so it is necessary to consider ways to prevent these events from appearing in the residual. In this chapter, the sinusoidal model is reinterpreted in terms of expansion functions; the structure of these expansion functions both indicates why the model breaks down for time-localized events and suggests methods to improve the model by casting it in a multiresolution framework. Two approaches are considered: applying the sinusoidal model to filter bank subbands, and using signal-adaptive analysis and synthesis frame sizes. These specific methods are discussed after a consideration of multiresolution as exemplified by the discrete wavelet transform.

The failure of not having seen is nothing like the failure of not having looked. -Pamela Alexander, “The Catacombs Again”