Download Resolving Wave Digital Filters with Multiple/Multiport Nonlinearities
We present a novel framework for developing Wave Digital Filter (WDF) models from reference circuits with multiple/multiport nonlinearities. Collecting all nonlinearities into a vector at the root of a WDF tree bypasses the traditional WDF limitation to a single nonlinearity. The resulting system has a complicated scattering relationship between the nonlinearity ports and the ports of the rest of the (linear) circuit, which can be solved by a Modified-NodalAnalysis-derived method. For computability reasons, the scattering and vector nonlinearity must be solved jointly; we suggest a derivative of the K-method. This novel framework significantly expands the class of appropriate WDF reference circuits. A case study on a clipping stage from the Big Muff Pi distortion pedal involves both a transistor and a diode pair. Since it is intractable with standard WDF methods, its successful simulation demonstrates the usefulness of the novel framework.
Download Signal Decorrelation using Perceptually Informed Allpass Filters
When a monophonic source signal is projected from two or more loudspeakers, listeners typically perceive a single, phantom source, positioned according to the relative signal amplitudes and speaker locations. While this property is the basis of modern panning algorithms, it is often desirable to control the perceived spatial extent of the phantom source, or to project multiple, separately perceived copies of the signal. So that the human auditory system does not process the loudspeaker outputs as a single coherent source, these effects are commonly achieved by generating a set of mutually decorrelated (e.g., statistically independent) versions of the source signal, which are then panned to make an extended source or multiple, independent source copies. In this paper, we introduce an approach to decorrelation using randomly generated allpass filters, and introduce numerical methods for evaluating the perceptual effectiveness of decorrelation algorithms. By using allpass filters, the signal magnitude is preserved, and the decorrelated copies and original signal will be perceptually very similar. By randomly selecting the magnitude and frequency of the poles of each allpass biquad section in the decorrelating filter, multiple decorrelating filters may be generated that maintain a degree of statistical independence. We present results comparing our approach (including methods for choosing the number of biquad sections and designing the statistics of the pole locations) to several established decorrelation methods discussed in the literature.
Download Extensions and Applications of Modal Dispersive Filters
Dispersive delay and comb filters, implemented as a parallel sum of high-Q mode filters tuned to provide a desired frequency-dependent delay characteristic, have advantages over dispersive filters that are implemented using cascade or frequency-domain architectures. Here we present techniques for designing the modal filter parameters for music and audio applications. Through examples, we show that this parallel structure is conducive to interactive and time-varying modifications, and we introduce extensions to the basic model.
Download Real-Time Modal Synthesis of Crash Cymbals with Nonlinear Approximations, Using a GPU
We apply modal synthesis to create a virtual collection of crash cymbals. Synthesizing each cymbal may require enough modes to stress a modern CPU, so a full drum set would certainly not be tractable in real-time. To work around this, we create a GPU-accelerated modal filterbank, with each individual set piece allocated over two thousand modes. This takes only a fraction of available GPU floating-point throughput. With CPU resources freed up, we explore methods to model the different instrument response in the linear/harmonic and non-linear/inharmonic regions that occur as more energy is present in a cymbal: a simple approach, yet one that preserves the parallelism of the problem, uses multisampling, and a more physically-based approach approximates modal coupling.
Download Delay Network Architectures for Room and Coupled Space Modeling
Feedback delay network reverberators have decay filters associated with each delay line to model the frequency dependent reverberation time (T60) of a space. The decay filters are typically designed such that all delay lines independently produce the same T60 frequency response. However, in real rooms, there are multiple, concurrent T60 responses that depend on the geometry and physical properties of the materials present in the rooms. In this paper, we propose the Grouped Feedback Delay Network (GFDN), where groups of delay lines share different target T60s. We use the GFDN to simulate coupled rooms, where one room is significantly larger than the other. We also simulate rooms with different materials, with unique decay filters associated with each delay line group, designed to represent the T60 characteristics of a particular material. The T60 filters are designed to emulate the materials’ absorption characteristics with minimal computation. We discuss the design of the mixing matrix to control inter- and intra-group mixing, and show how the amount of mixing affects behavior of the room modes. Finally, we discuss the inclusion of air absorption filters on each delay line and physically motivated room resizing techniques with the GFDN.
Download Probabilistic Reverberation Model Based on Echo Density and Kurtosis
This article proposes a probabilistic model for synthesizing room impulse responses (RIRs) for use in convolution artificial reverberators. The proposed method is based on the concept of echo density. Echo density is a measure of the number of echoes per second in an impulse response and is a demonstrated perceptual metric of artificial reverberation quality. As echo density is related to the statistical measure of kurtosis, this article demonstrates that the statistics of an RIR can be modeled using a probabilistic mixture model. A mixture model designed specifically for modeling RIRs is proposed. The proposed method is useful for statistically replicating RIRs of a measured environment, thereby synthesizing new independent observations of an acoustic space. A perceptual pilot study is carried out to evaluate the fidelity of the replication process in monophonic and stereo artificial reverberators.