Estimates of the Reconstruction Error in Partially Redressed Warped Frames Expansions
In recent work, redressed warped frames have been introduced for the analysis and synthesis of audio signals with nonuniform frequency and time resolutions. In these frames, the allocation of frequency bands or time intervals of the elements of the representation can be uniquely described by means of a warping map. Inverse warping applied after time-frequency sampling provides the key to reduce or eliminate dispersion of the warped frame elements in the conjugate variable, making it possible, e.g., to construct frequency warped frames with synchronous time alignment through frequency. The redressing procedure is however exact only when the analysis and synthesis windows have compact support in the domain where warping is applied. This implies that frequency warped frames cannot have compact support in the time domain. This property is undesirable when online computation is required. Approximations in which the time support is finite are however possible, which lead to small reconstruction errors. In this paper we study the approximation error for compactly supported frequency warped analysis-synthesis elements, providing a few examples and case studies.