Zdenek Prusa

A Noniterative Method for Reconstruction of Phase From STFT Magnitude

A noniterative method for the reconstruction of the short-time fourier transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the un-sampled STFT with respect to the Gaussian window. Although the theory holds in the continuous setting only, the experiments show that the algorithm performs well even in the discretized setting (discrete Gabor transform) with low redundancy using the sampled Gaussian window, the truncated Gaussian window and even other compactly supported windows such as the Hann window. Due to the noniterative nature, the algorithm is very fast and it is suitable for long audio signals. Moreover, solutions of iterative phase reconstruction algorithms can be improved considerably by initializing them with the phase estimate provided by the present algorithm. We present an extensive comparison with the state-of-the-art algorithms in a reproducible manner.

Reassignment and synchrosqueezing for general time-frequency filter banks, subsampling and processing

In this contribution, we extend the reassignment method (RM) and synchrosqueezing transform (SST) to arbitrary time-frequency localized filters and, in the first case, arbitrary decimation factors. A sufficient condition for the invertibility of the SST is provided. RM and SST are techniques for deconvolution of short-time Fourier and wavelet representations. In both methods, the partial phase derivatives of a complex-valued time-frequency representation are used to determine the instantaneous frequency and group delay associated to the individual representation coefficients. Subsequently, the coefficient energy is reassigned to the determined position. Combining RM and frame theory, we propose a processing scheme that benefits both from the improved localization of the reassigned representation and the frame properties of the underlying complex-valued representation. This scheme is particularly interesting for applications that require low redundancy not achievable by an invertible SST.

Phase vocoder done right

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.

Toward High-Quality Real-Time Signal Reconstruction From STFT Magnitude

An efficient algorithm for real-time signal reconstruction from the magnitude of the short-time Fourier transform (STFT) is introduced. The proposed approach combines the strengths of two previously published algorithms: the real-time phase gradient heap integration and the Gnann and Spiertzs real-time iterative spectrogram inversion with look-ahead. An extensive comparison with the state-of-the-art algorithms in a reproducible manner is presented.

Acceleration of audio inpainting by support restriction

We present a simple algorithm which accelerates the sparsity-based audio inpainting. The algorithm optimally restricts the signal support around the missing data region. This way, increased computational efficiency is achieved by avoiding inclusion of unnecessary values in the optimization process. For testing purposes, we use the discrete Gabor transform as the sparsity promoting representation, but the method can be easily translated to other systems.

Non-iterative filter bank phase (re)construction

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.

Segmented computation of wavelet transform via lifting scheme

This paper presents a novel algorithm for segmented (segmentwise) computation of forward and inverse wavelet transform via a lifting scheme, applicable to any type of a lifting scheme representation of wavelets. The main idea is to process segments taken from a long one-dimensional signal so that after reconstruction, no border distortion between segments occurs. This is achieved by means of sophisticated segment overlapping. In this work, arbitrary and possibly varying segment lengths are considered. The derivation of formulas for overlap enumeration is the main concern of this work. The algorithm produces sets of coefficients for each segment. These sets from each segment ordered correctly are exactly the same coefficients the whole signal discrete wavelet transform results in. Similarly, the whole signal inverse discrete wavelet transform is equal to applying the algorithm to sets of coefficients and overlapping the results accordingly. The algorithm makes it possible to process signals in realtime, allows coarse parallelization since the computation on the particular segments is independent and also allows computation of wavelet transform on devices with a limited amount of memory.