Oral Session 1: Digital Signal Processing

09:20-10:40 on Tuesday, 3rd September

P350 Lecture Theatre, Parkside

Chiar: Udo Zölzer
Non-Iterative Phaseless Reconstruction From Wavelet Transform Magnitude
Nicki Holighaus, Günther Koliander, Zdenek Prusa and Luis Daniel Abreu

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.

View Paper
High-Definition Time-Frequency Representation Based on Adaptive Combination of Fan-Chirp Transforms via Structure Tensor
Maurício Do Vale Madeira da Costa and Luiz Wagner Pereira Biscainho

This paper presents a novel technique for producing high-definition time-frequency representations by combining different instances of short-time fan-chirp transforms. The proposed method uses directional information provided by an image processing technique named structure tensor, applied over a spectrogram of the input signal. This information indicates the best analysis window size and chirp parameter for each time-frequency bin, and feeds a simple interpolation procedure, which produces the final representation. The method allows the proper representation of more than one sound source simultaneously via fan-chirp transforms with different resolutions, and provides a precise reproduction of transient information. Experiments in both synthetic and real audio illustrate the performance of the proposed system.

View Paper
Non-Iterative Solvers For Nonlinear Problems: The Case of Collisions
Michele Ducceschi and Stefan Bilbao

Nonlinearity is a key feature in musical instruments and electronic circuits alike, and thus in simulation, for the purposes of physics-based modeling and virtual analog emulation, the numerical solution of nonlinear differential equations is unavoidable. Ensuring numerical stability is thus a major consideration. In general, one may construct implicit schemes using well-known discretisation methods such as the trapezoid rule, requiring computationally-costly iterative solvers at each time step. Here, a novel family of provably numerically stable time-stepping schemes is presented, avoiding the need for iterative solvers, and thus of greatly reduced computational cost. An application to the case of the collision interaction in musical instrument modeling is detailed.

View Paper
Generalizations of Velvet Noise and their Use in 1-Bit Music
Kurt Werner

A family of spectrally-flat noise sequences called “Velvet Noise” have found use in reverb modeling, decorrelation, speech synthesis, and abstract sound synthesis. These noise sequences are ternary—they consist of only the values −1, 0, and +1. They are also sparse in time, with pulse density being their main design parameter, and at typical audio sampling rates need only several thousand non-zero samples per second to sound “smooth.” This paper proposes “Crushed Velvet Noise” (CVN) generalizations to the classic family of Velvet Noise sequences including “Original Velvet Noise” (OVN), “Additive Random Noise” (ARN), and “Totally Random Noise” (TRN). In these generalizations, the probability of getting a positive or negative impulse is a free parameter. Manipulating this probability gives Crushed OVN and ARN low-shelf spectra rather than the flat spectra of standard Velvet Noise, while the spectrum of Crushed TRN is still flat. This new family of noise sequences is still ternary and sparse in time. However, pulse density now controls the shelf cutoff frequency, and the distribution of polarities controls the shelf depth. Crushed Velvet Noise sequences with pulses of only a single polarity are particularly useful in a niche style of music called “1- bit music”: music with a binary waveform consisting of only 0s and 1s. We propose Crushed Velvet Noise as a valuable tool in 1- bit music composition, where its sparsity allows for good approximations to operations, such as addition, which are impossible for signals in general in the 1-bit domain.

View Paper