The paper presents a variant of the segmentwise wavelet transform (blockwise DWT, online DWT or SegDWT) algorithm adapted to real-time audio processing. The implementation of the algorithm as a VST plugin is presented as well. The main problem of segmentwise wavelet coefficient processing is the handling of the segment borders. The common border extension methods result in “false” coefficients, which in turn result in border distortion (block-end effects) after particular types of coefficient processing. In contrast, the SegDWT algorithm employs a segment extension technique to prevent this inconvenience and produce exactly the same coefficients as the wavelet transform of the whole signal would do. In this paper we remove some of the shortcomings of the original SegDWT algorithm; for example the need for the “right” segment extension is canceled. The VST plugin module created is described from the viewpoints of both the user and the programmer; the latter can easily add their own method for processing the coefficients.

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In this work, we present an algorithm for phaseless reconstruction from magnitude-only wavelet coefficients. The method relies on an explicit relation between the log-magnitude and phase gradients of analytic wavelet transforms and an extension of the Phase-Gradient Heap Integration (PGHI) algorithm recently introduced for Gabor phaseless reconstruction. This relation is exact for a certain family of mother wavelets including Cauchy wavelets of arbitrary order, but only holds approximately otherwise. The presented experiments show that, in practice, the proposed wavelet PGHI method provides competitive quality for various mother wavelets. Furthermore, wavelet PGHI is a non-iterative scheme and thus computational performance is significantly better than established alternate projection methods.

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