Download A frequency tracker based on a Kalman filter update of a single parameter adaptive notch filter In designing a frequency tracker, the goal is to follow the continual time variation of the frequency from a particular sinusoidal component in a noisy signal with a high accuracy and a low sample delay. Although there exists a plethora of frequency trackers in the literature, in this paper, we focus on the particular class of frequency trackers that are built upon an adaptive notch filter (ANF), i.e. a constrained bi-quadratic infinite impulse response filter, where only a single parameter needs to be estimated. As opposed to using the conventional least-mean-square (LMS) algorithm, we present an alternative approach for the estimation of this parameter, which ultimately corresponds to the frequency to be tracked. Specifically, we reformulate the ANF in terms of a state-space model, where the state contains the unknown parameter and can be subsequently updated using a Kalman filter. We also demonstrate that such an approach is equivalent to doing a normalized LMS filter update, where the regularization parameter can be expressed as the ratio of the variance of the measurement noise to the variance of the prediction error. Through an evaluation with both simulated and realistic data, it is shown that in comparison to the LMS-updated frequency tracker, the proposed Kalmanupdated alternative, results in a more accurate performance, with a faster convergence rate, while maintaining a low computational complexity and the ability to be updated on a sample-by-sample basis.
Download Nonlinear Strings based on Masses and Springs Due to advances in computational power, physical modelling for sound synthesis has gained an increased popularity over the past decades. Although much work has been done to accurately simulate existing physical systems, much less work exists on the use of physical modelling simply for the sake of creating sonically interesting sounds. This work presents a mass-spring network, inspired by existing models of the physical string. Masses have 2 translational degrees of freedom (DoF), and the springs have an additional equilibrium separation term, which together result in highly nonlinear effects. The main aim of this work is to create sonically interesting sounds while retaining some of the natural qualities of the physical string, as opposed to accurately simulating it. Although the implementation exhibits chaotic behaviour for certain choices of parameters, the presented system can create sonically interesting timbres, including nonlinear pitch glides and ‘wobbles’.
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.
Download Fully Conditioned and Low-Latency Black-Box Modeling of Analog Compression Neural networks have been found suitable for virtual analog modeling applications. Several analog audio effects have been successfully modeled with deep learning techniques, using low-latency and conditioned architectures suitable for real-world applications. Challenges remain with effects presenting more complex responses, such as nonlinear and time-varying input-output relationships. This paper proposes a deep-learning model for the analog compression effect. The architecture we introduce is fully conditioned by the device control parameters and it works on small audio segments, allowing low-latency real-time implementations. The architecture is used to model the CL 1B analog optical compressor, showing an overall high accuracy and ability to capture the different attack and release compression profiles. The proposed architecture’ ability to model audio compression behaviors is also verified using datasets from other compressors. Limitations remain with heavy compression scenarios determined by the conditioning parameters.
Download Low-cost Numerical Approximation of HRTFs: a Non-Linear Frequency Sampling Approach Head-related transfer functions (HRTFs) describe filters that model the scattering effect of the human body on sound waves. In their discrete-time form, they are used in acoustic simulations for virtual reality (VR) or augmented reality (AR), and since HRTFs are listener-specific, the use of individualized HRTFs allows achieving more realistic perceptual results. One way to produce individualized HRTFs is by estimating the sound field around the subjects’ 3D representations (meshes) via numerical simulations, which compute discrete complex pressure values in the frequency domain in regular frequency steps. Despite the advances in the area, the computational resources required for this process are still considerably high and increase with frequency. The goal of this paper is to tackle the high computational cost associated with this task by sampling the frequency domain using hybrid linear-logarithmic frequency resolution. The results attained in simulations performed using 23 real 3D meshes suggest that the proposed strategy is able to reduce the computational cost while still providing remarkably low spectral distortion, even in simulations that require as little as 11.2% of the original total processing time.
Download A Differentiable Digital Moog Filter For Machine Learning Applications In this project, a digital ladder filter has been investigated and expanded. This structure is a simplified digital analog model of the well known analog Moog ladder filter. The goal of this paper is to derive the differentiation expressions of this filter with respect to its control parameters in order to integrate it in machine learning systems. The derivation of the backpropagation method is described in this work, it can be generalized to a Moog filter or a similar filter having any number of stages. Subsequently, the example of an adaptive Moog filter is provided. Finally, a machine learning application example is shown where the filter is integrated in a deep learning framework.
Download A Quadric Surface Model of Vacuum Tubes for Virtual Analog Applications Despite the prevalence of modern audio technology, vacuum tube amplifiers continue to play a vital role in the music industry. For this reason, over the years, many different digital techniques have been introduced for accomplishing their emulation. In this paper, we propose a novel quadric surface model for tube simulations able to overcome the Cardarilli model in terms of efficiency whilst retaining comparable accuracy when grid current is negligible. After showing the model capability to well outline tubes starting from measurement data, we perform an efficiency comparison by implementing the considered tube models as nonlinear 3-port elements in the Wave Digital domain. We do this by taking into account the typical common-cathode gain stage employed in vacuum tube guitar amplifiers. The proposed model turns out to be characterized by a speedup of 4.6× with respect to the Cardarilli model, proving thus to be promising for real-time Virtual Analog applications.
Download Real-Time Modal Synthesis of Nonlinearly Interconnected Networks Modal methods are a long-established approach to physical modeling sound synthesis. Projecting the equation of motion of a linear, time-invariant system onto a basis of eigenfunctions yields a set of independent forced, lossy oscillators, which may be simulated efficiently and accurately by means of standard time-stepping methods. Extensions of modal techniques to nonlinear problems are possible, though often requiring the solution of densely coupled nonlinear time-dependent equations. Here, an application of recent results in numerical simulation design is employed, in which the nonlinear energy is first quadratised via a convenient auxiliary variable. The resulting equations may be updated in time explicitly, thus avoiding the need for expensive iterative solvers, dense linear system solutions, or matrix inversions. The case of a network of interconnected distributed elements is detailed, along with a real-time implementation as an audio plugin.
Download Tunable Collisions: Hammer-String Simulation with Time-Variant Parameters In physical modelling synthesis, articulation and tuning are effected via time-variation in one or more parameters. Adopting hammered strings as a test case, this paper develops extended forms of such control, proposing a numerical formulation that affords online adjustment of each of its scaled-form parameters, including those featuring in the one-sided power law for modelling hammerstring collisions. Starting from a modally-expanded representation of the string, an explicit scheme is constructed based on quadratising the contact energy. Compared to the case of time-invariant contact parameters, updating the scheme’s state variables relies on the evaluation of two additional analytic partial derivatives of the auxiliary variable. A numerical energy balance is derived and the numerical contact force is shown to be strictly non-adhesive. Example results with time-variant tension and time-variant contact stiffness are detailed, and real-time viability is demonstrated.
Download Real-time Gong Synthesis Physical modeling sound synthesis is notoriously computationally intensive. But recent advances in algorithm efficiency, accompanied by increases in available computing power have brought real-time performance within range for a variety of complex physical models. In this paper, the case of nonlinear plate vibration, used as a simple model for the synthesis of sounds from gongs is considered. Such a model, derived from that of Föppl and von Kármán, includes a strong geometric nonlinearity, leading to a variety of perceptually-salient effects, including pitch glides and crashes. Also discussed here are input excitation and scanned multichannel output. A numerical scheme is presented that mirrors the energetic and dissipative properties of a continuous model, allowing for control over numerical stability. Furthermore, the nonlinearity in the scheme can be solved explicitly, allowing for an efficient solution in real time. The solution relies on a quadratised expression for numerical energy, and is in line with recent work on invariant energy quadratisation and scalar auxiliary variable approaches to simulation. Implementation details, including appropriate perceptuallyrelevant choices for parameter settings are discussed. Numerical examples are presented, alongside timing results illustrating realtime performance on a typical CPU.