Time-Width Versus Frequency Band Mapping of Energy Distributions

Most of the signal processing operations involve some kind of a transformation or approximation of the signal. The transform coefficients or the approximation parameters reveal many hidden characteristics of a signal that can be appropriately processed to extract useful information. In recent years, adaptive time-frequency (TF) transformations have significantly contributed to this area. The TF transformation can be classified into two main categories based on 1) signal decomposition approaches and 2) bilinear TF distributions (also known as Cohen´s class). TF distributions are nonparametric in nature and mainly used for visualization purposes. On the other hand, decomposition approaches are parametric in nature and highly suitable for objective feature extraction. This paper focuses on a particular TF decomposition approach (adaptive TF transformation) based on matching pursuit-type algorithm. Using this decomposition approach, a novel time-width versus frequency band (TWFB) energy mapping is proposed that possesses both parameterization benefits and meaningful visual patterns with favorable properties for pattern recognition. This organized mapping of the TF decomposition parameters allows the application of pruning algorithms such as local discriminant bases (LDB) to identify application specific TF subspaces. The identification of these subspaces enables efficient processing of information and reduces the computational effort considerably. The visual patterns of the TWFB mappings exhibit high potential of becoming a powerful pattern analysis tool. The paper covers in detail the formulation of the TWFB mapping and some of its properties. Experiments performed with speech and synthetic signals produced desirable results demonstrating the benefits of TWFB for pattern recognition related applications