Zdeněk Průša

Zdeněk Průša, Nicki Holighaus

Signal reconstruction from magnitude-only measurements presents a long-standing problem in signal processing. In this contribution, we propose a phase (re)construction method for filter banks with uniform decimation and controlled frequency variation. The suggested procedure extends the recently introduced phase-gradient heap integration and relies on a phase-magnitude relationship for filter bank coefficients obtained from Gaussian filters. Admissible filter banks are modeled as the discretization of certain generalized translation-invariant systems, for which we derive the phase-magnitude relationship explicitly. The implementation for discrete signals is described and the performance of the algorithm is evaluated on a range of real and synthetic signals.

Zdenek Prusa, Nicki Holighaus

The phase vocoder (PV) is a widely spread technique for processing audio signals. It employs a short-time Fourier transform (STFT) analysis-modify-synthesis loop and is typically used for time-scaling of signals by means of using different time steps for STFT analysis and synthesis. The main challenge of PV used for that purpose is the correction of the STFT phase. In this paper, we introduce a novel method for phase correction based on phase gradient estimation and its integration. The method does not require explicit peak picking and tracking nor does it require detection of transients and their separate treatment. Yet, the method does not suffer from the typical phase vocoder artifacts even for extreme time stretching factors.

Thibaud Necciari, Nicki Holighaus, Peter Balazs et al.

Many audio applications rely on filter banks (FBs) to analyze, process, and re-synthesize sounds. To approximate the auditory frequency resolution in the signal chain, some applications rely on perceptually motivated FBs, the gammatone FB being a popular example. However, most perceptually motivated FBs only allow partial signal reconstruction at high redundancies and/or do not have good resistance to sub-channel processing. This paper introduces an oversampled perceptually motivated FB enabling perfect reconstruction, efficient FB design, and adaptable redundancy. The filters are directly constructed in the frequency domain and linearly distributed on a perceptual frequency scale (e.g. ERB, Bark, or Mel scale). The proposed design allows for various filter shapes, uniform or non-uniform FB setting, and large down-sampling factors. For redundancies $\geq$ 3 perfect reconstruction is achieved by computing the canonical dual FB analytically. For lower redundancies perfect reconstruction is achieved using an iterative method. Experiments show performance improvements of the proposed approach when compared to the gammatone FB in terms of reconstruction error and resistance to sub-channel processing, especially at low redundancies.