An efficient and perfectly invertible signal transform featuring a constant-Q frequency resolution is presented. The proposed approach is based on the idea of the recently introduced nonstationary Gabor frames. Exploiting the properties of the operator corresponding to a family of analysis atoms, this approach overcomes the problems of the classical implementations of constant-Q transforms, in particular, computational intensity and lack of invertibility. Perfect reconstruction is guaranteed by using an easy to calculate dual system in the synthesis step and computation time is kept low by applying FFT-based processing. The proposed method is applied to real-life signals and evaluated in comparison to a related approach, recently introduced specifically for audio signals.

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Filter banks, both uniform and non-uniform, are widely used for signal analysis and processing. However, the application of a timefrequency localized filter inevitably causes some amount of spectral and temporal leakage that, simultaneously, cannot be arbitrarily reduced. Reassignment is a classical procedure to eliminate this leakage in short-time Fourier spectrograms, thereby providing a sharper, more exact time-frequency domain signal representation. The reassignment technique was recently generalized to general filter banks, opening new possibilities for its application in signal analysis and processing. We present here the very first implementation of filter bank reassignment in a real-time analysis setting, more specifically as visualization in a basic audio player application. The visualization provides a low delay moving spectrogram with respect to virtually any time-frequency filter bank by interfacing the C backend of the LTFAT open-source toolbox for time-frequency processing. Low delay is achieved by blockwise processing, implemented with the JUCE C++ Library.

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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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Matching pursuit (MP) algorithms are widely used greedy methods to find K-sparse signal approximations in redundant dictionaries. We present an acceleration technique and an implementation of the matching pursuit algorithm acting on a multi-Gabor dictionary, i.e., a concatenation of several Gabor-type time-frequency dictionaries, consisting of translations and modulations of possibly different windows, time- and frequency-shift parameters. The proposed acceleration is based on pre-computing and thresholding inner products between atoms and on updating the residual directly in the coefficient domain, i.e., without the round-trip to the signal domain. Previously, coefficient-domain residual updates have been dismissed as having prohibitive memory requirements. By introducing an approximate update step, we can overcome this restriction and greatly improve the performance of matching pursuit at a modest cost in terms of approximation quality per selected atom. An implementation in C with Matlab and GNU Octave interfaces is available, outperforming the standard Matching Pursuit Toolkit (MPTK) by a factor of 3.5 to 70 in the tested conditions. Additionally, we provide experimental results illustrating the convergence of the implementation.

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