An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Basic Filters for Convolutional Neural Networks Applied to Music: Training or Design?

When convolutional neural networks are used to tackle learning problems based on music or, more generally, time series data, raw one-dimensional data are commonly pre-processed to obtain spectrogram or mel-spectrogram coefficients, which are then used as input to the actual neural network. In this contribution, we investigate, both theoretically and experimentally, the influence of this pre-processing step on the network's performance and pose the question, whether replacing it by applying adaptive or learned filters directly to the raw data, can improve learning success. The theoretical results show that approximately reproducing mel-spectrogram coefficients by applying adaptive filters and subsequent time-averaging is in principle possible. We also conducted extensive experimental work on the task of singing voice detection in music. The results of these experiments show that for classification based on Convolutional Neural Networks the features obtained from adaptive filter banks followed by time-averaging perform better than the canonical Fourier-transform-based mel-spectrogram coefficients. Alternative adaptive approaches with center frequencies or time-averaging lengths learned from training data perform equally well.Comment: Completely revised version; 21 pages, 4 figure

Sparse and Cosparse Audio Dequantization Using Convex Optimization

The paper shows the potential of sparsity-based methods in restoring quantized signals. Following up on the study of Brauer et al. (IEEE ICASSP 2016), we significantly extend the range of the evaluation scenarios: we introduce the analysis (cosparse) model, we use more effective algorithms, we experiment with another time-frequency transform. The paper shows that the analysis-based model performs comparably to the synthesis-model, but the Gabor transform produces better results than the originally used cosine transform. Last but not least, we provide codes and data in a reproducible way

Superposition frames for adaptive time-frequency analysis and fast reconstruction

In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the extant literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that this construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio

Nonlinear approximation with nonstationary Gabor frames

We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions generalizes to the nonstationary case, providing perfect reconstruction and an FFT based implementation for compactly supported window functions sampled at a certain density. It is also known that for some signal classes, NSGFs with flexible time resolution tend to provide sparser expansions than can be obtained with classical Gabor frames. In this article we show, for the continuous case, that sparseness of a nonstationary Gabor expansion is equivalent to smoothness in an associated decomposition space. In this way we characterize signals with sparse expansions relative to NSGFs with flexible time resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding the coefficients of both stationary and nonstationary Gabor expansions.Comment: 19 pages, 2 figure

Introducing Latent Timbre Synthesis

We present the Latent Timbre Synthesis (LTS), a new audio synthesis method using Deep Learning. The synthesis method allows composers and sound designers to interpolate and extrapolate between the timbre of multiple sounds using the latent space of audio frames. We provide the details of two Variational Autoencoder architectures for LTS, and compare their advantages and drawbacks. The implementation includes a fully working application with graphical user interface, called \textit{interpolate\_two}, which enables practitioners to explore the timbre between two audio excerpts of their selection using interpolation and extrapolation in the latent space of audio frames. Our implementation is open-source, and we aim to improve the accessibility of this technology by providing a guide for users with any technical background