The familiar “crackling” is one of the undesirable phenomena which we deal with in an LP record. Wavelet analysis brings a new alternative approach to the removal of this feature in the restoration process of the recording. In the paper, the principle of this method is described. A theoretical discussion of how the selection of the wavelet basis affects the quality of the restoration is also included.

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In audio applications it is often necessary to process the signal in “real time”. The method of segmented wavelet transform (SegWT) makes it possible to compute the discrete-time wavelet transform of a signal segment-by-segment, not using the classical “windowing”. This means that the method could be utilized for wavelettype processing of an audio signal in real time, or alternatively in case we just need to process a long signal, but there is insufficient computational memory capacity for it (e.g. in the DSPs). In the paper, the principle of the segmented forward wavelet transform is explained and the algorithm is described in detail.

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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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The paper presents a unified, flexible framework for the tasks of audio inpainting, declipping, and dequantization. The concept is further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the signal’s time-frequency coefficients. The task of reconstructing an audio signal from degraded observations in two different domains is formulated as an inverse problem, and several algorithmic solutions are developed. The viability of the presented concept is demonstrated on an example where audio reconstruction from partial and quantized observations of both the time-domain signal and its time-frequency coefficients is carried out.

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