Multiresolution sinusoidal modeling using adaptive segmentation

The sinusoidal model has proven useful for representation and modi cation of speech and audio. One drawback, however, is that a sinusoidal signal model is typically derived using a xed frame size, which corresponds to a rigid signal segmentation. For nonstationary signals, the resolution limitations that result from this rigidity lead to reconstruction artifacts. It is shown in this paper that such artifacts can be signi cantly reduced by using a signaladaptive segmentation derived by a dynamic program. An atomic interpretation of the sinusoidal model is given; this perspective suggests that algorithms for adaptive segmentation can be viewed as methods for adapting the time scales of the constituent atoms so as to improve the model by employing appropriate time-frequency tradeo s. 1. ADAPTIVE SIGNAL MODELS Compact signal models are useful for analysis, compression, enhancement, and modi cation [1]. To achieve compaction for arbitrary signals, models must be constructed in a signal-adaptive manner. Such signal adaptivity is the central principle in methods such as best bases [2], adaptive wavelet packets [3], and various atomic decomposition approaches such as matching pursuit [4, 5]; these models can be interpreted as signal expansions in which the expansion functions are chosen in a signal-adaptive fashion from an overcomplete set [1]. Signal adaptivity can also be achieved in parametric methods such as the sinusoidal model, in which the sinusoidal expansion functions are constructed using parameters extracted from the signal [1]. This paper is concerned with the sinusoidal model. The basic problem is that the sinusoidal model is typically carried out with a xed frame size which may not be appropriate for all regions of a nonstationary signal. It is demonstrated that a xed signal segmentation leads to resolution limitations that result in artifacts such as pre-echo, which is a well-known di culty in audio coding [6]. An atomic interpretation of the sinusoidal model suggests that these reconstruction artifacts can be reduced by adapting the time scales of the atoms according to the signal behavior, i.e. using long scales for stationary behavior and short scales for transients. It is demonstrated that such adaptation can be carried out e ectively using a segmentation algorithm based on a dynamic program. Analysis windows