We propose a new algorithm for time stretching music signals based on the theory of nonstationary Gabor frames (NSGFs). The algorithm extends the techniques of the classical phase vocoder (PV) by incorporating adaptive time-frequency (TF) representations and adaptive phase locking. The adaptive TF representations imply good time resolution for the onsets of attack transients and good frequency resolution for the sinusoidal components. We estimate the phase values only at peak channels and the remaining phases are then locked to the values of the peaks in an adaptive manner. During attack transients we keep the stretch factor equal to one and we propose a new strategy for determining which channels are relevant for reinitializing the corresponding phase values. In contrast to previously published algorithms we use a non-uniform NSGF to obtain a low redundancy of the corresponding TF representation. We show that with just three times as many TF coefficients as signal samples, artifacts such as phasiness and transient smearing can be greatly reduced compared to the classical PV. The proposed algorithm is tested on both synthetic and real-world signals and compared with state-of-the-art algorithms in a reproducible manner.

The application of adaptive, time-frequency based signal analysis has recently attracted increasing attention. While using adapted time-frequency atoms has shown promising results for example in audio processing, the reconstruction from the corresponding analysis coefficients usually exhibits significant error. In this contribution we propose a method to reduce the reconstruction error by using modified time-frequency atoms in the transition region between adjacent areas of time-frequency adaptation. The modification is obtained by projecting the relevant atoms onto a system of weighted vectors which are optimally concentrated inside the desired regions of adaptation. We give a theoretical derivation of the improvement of error and illustrate our method with numerical examples.

We consider the audio declipping problem by using iterative thresholding algorithms and the principle of social sparsity. This recently introduced approach features thresholding/shrinkage operators which allow to model dependencies between neighboring coefficients in expansions with time-frequency dictionaries. A new unconstrained convex formulation of the audio declipping problem is introduced. The chosen structured thresholding operators are the so called windowed group-Lasso and the persistent empirical Wiener. The usage of these operators significantly improves the quality of the reconstruction, compared to simple soft-thresholding. The resulting algorithm is fast, simple to implement, and it outperforms the state of the art in terms of signal to noise ratio.

Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency bands is preferable. This paper introduces a framework for efficient implementation of invertible signal transforms allowing for non-uniform frequency resolution. Non-uniformity in frequency is realized by applying nonstationary Gabor frames with adaptivity in the frequency domain. The realization of a perfectly invertible constant-Q transform is described in detail. To achieve real-time processing, independent of signal length, slice-wise processing of the full input signal is proposed and referred to as sliCQ transform. By applying frame theory and FFT-based processing, the presented approach overcomes computational inefficiency and lack of invertibility of classical constant-Q transform implementations. Numerical simulations evaluate the efficiency of the proposed algorithm and the method's applicability is illustrated by experiments on real-life audio signals .

Exponential sweeps are widely used to measure impulse responses of electro-acoustic systems. Measurements are often contaminated by environmental noise and nonlinear distortions. We propose a method to increase the signal-to-noise ratio (SNR) by denoising the recorded signal in the time-frequency plane. In contrast to state-of-the art denoising methods, no assumption about the spectral characteristics of the noise is required. Numerical simulations demonstrate improvements in the SNR under low-SNR conditions even for measurements contaminated by colored noise.