Percussion synthesis based on models of nonlinear shell vibration

The synthesis of sound based on physical models of 2-D percussion instruments is problematic and has been approached only infrequently in the literature. Beyond the computational expense inherent to the simulation of 2-D systems, a deeper difficulty is in dealing with the strong nonlinearity exhibited by thin structures when struck--this nonlinearity leads to phenomena which are not captured, even approximately, by a linear model, and nearly all synthesis work is based on the assumption that the distributed resonating component of a musical instrument is linear. Perceptually, the effects of the vibration of a thin structure at high amplitudes can be heard as crashes, pitch glides, and the slow buildup of high-frequency energy characteristic of gongs. A large family of instruments may be described, approximately, as circular thin shells, of approximately spherical geometry, in which case a tractable PDE description, described here, is available. Time-domain finite-difference schemes, in radial coordinates, are a suitable method for synthesis. Stability conditions, numerical boundary conditions both at the edge and center, and implementation details are discussed, and simulation results are presented, highlighting the various perceptual effects mentioned above

Efficient synthesis of tension modulation in strings and membranes based on energy estimation

String and membrane vibrations cannot be considered as linear above a certain amplitude due to the variation in string or membrane tension. A relevant special case is when the tension is spatially constant and varies in time only in dependence of the overall string length or membrane surface. The most apparent perceptual effect of this tension modulation phenomenon is the exponential decay of pitch in time. Pitch glides due to tension modulation are an important timbral characteristic of several musical instruments, including the electric guitar and tom-tom drum, and many ethnic instruments. This paper presents a unified formulation to the tension modulation problem for onedimensional (1-D) (string) and two-dimensional (2-D) (membrane) cases. In addition, it shows that the short-time average of the tension variation, which is responsible for pitch glides, is approximately proportional to the system energy. This proportionality allows the efficient physics-based sound synthesis of pitch glides. The proposed models require only slightly more computational resources than linear models as opposed to earlier tension-modulated models of higher complexity

Model-based digital pianos: from physics to sound synthesis

International audiencePiano is arguably one of the most important instruments in Western music due to its complexity and versatility. The size, weight, and price of grand pianos, and the relatively simple control surface (keyboard) have lead to the development of digital counterparts aiming to mimic the sound of the acoustic piano as closely as possible. While most commercial digital pianos are based on sample playback, it is also possible to reproduce the sound of the piano by modeling the physics of the instrument. The process of physical modeling starts with first understanding the physical principles, then creating accurate numerical models, and finally finding numerically optimized signal processing models that allow sound synthesis in real time by neglecting inaudible phenomena, and adding some perceptually important features by signal processing tricks. Accurate numerical models can be used by physicists and engineers to understand the functioning of the instrument, or to help piano makers in instrument development. On the other hand, efficient real-time models are aimed at composers and musicians performing at home or at stage. This paper will overview physics-based piano synthesis starting from the computationally heavy, physically accurate approaches and then discusses the ones that are aimed at best possible sound quality in real-time synthesis

Towards Real-Time Non-Stationary Sinusoidal Modelling of Kick and Bass Sounds for Audio Analysis and Modification

Sinusoidal Modelling is a powerful and flexible parametric method for analysing and processing audio signals. These signals have an underlying structure that modern spectral models aim to exploit by separating the signal into sinusoidal, transient, and noise components. Each of these can then be modelled in a manner most appropriate to that component's inherent structure. The accuracy of the estimated parameters is directly related to the quality of the model's representation of the signal, and the assumptions made about its underlying structure. For sinusoidal models, these assumptions generally affect the non-stationary estimates related to amplitude and frequency modulations, and the type of amplitude change curve. This is especially true when using a single analysis frame in a non-overlapping framework, where biased estimates can result in discontinuities at frame boundaries. It is therefore desirable for such a model to distinguish between the shape of different amplitude changes and adapt the estimation of this accordingly. Intra-frame amplitude change can be interpreted as a change in the windowing function applied to a stationary sinusoid, which can be estimated from the derivative of the phase with respect to frequency at magnitude peaks in the DFT spectrum. A method for measuring monotonic linear amplitude change from single-frame estimates using the first-order derivative of the phase with respect to frequency (approximated by the first-order difference) is presented, along with a method of distinguishing between linear and exponential amplitude change. An adaption of the popular matching pursuit algorithm for refining model parameters in a segmented framework has been investigated using a dictionary comprised of sinusoids with parameters varying slightly from model estimates, based on Modelled Pursuit (MoP). Modelling of the residual signal using a segmented undecimated Wavelet Transform (segUWT) is presented. A generalisation for both the forward and inverse transforms, for delay compensations and overlap extensions for different lengths of Wavelets and the number of decomposition levels in an Overlap Save (OLS) implementation for dealing with convolution block-based artefacts is presented. This shift invariant implementation of the DWT is a popular tool for de-noising and shows promising results for the separation of transients from noise