Title: Estimates of the Reconstruction Error in Partially Redressed Warped Frames Expansions,
Abstract: In recent work, redressed warped frames have been introduced for the analysis
and synthesis of audio signals with non-uniform 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.