14,482 research outputs found
Acoustic modeling using the digital waveguide mesh
The digital waveguide mesh has been an active area of music acoustics research for over ten years. Although founded in 1-D digital waveguide modeling, the principles on which it is based are not new to researchers grounded in numerical simulation, FDTD methods, electromagnetic simulation, etc. This article has attempted to provide a considerable review of how the DWM has been applied to acoustic modeling and sound synthesis problems, including new 2-D object synthesis and an overview of recent research activities in articulatory vocal tract modeling, RIR synthesis, and reverberation simulation. The extensive, although not by any means exhaustive, list of references indicates that though the DWM may have parallels in other disciplines, it still offers something new in the field of acoustic simulation and sound synth
Energy conserving schemes for the simulation of musical instrument contact dynamics
Collisions are an innate part of the function of many musical instruments.
Due to the nonlinear nature of contact forces, special care has to be taken in
the construction of numerical schemes for simulation and sound synthesis.
Finite difference schemes and other time-stepping algorithms used for musical
instrument modelling purposes are normally arrived at by discretising a
Newtonian description of the system. However because impact forces are
non-analytic functions of the phase space variables, algorithm stability can
rarely be established this way. This paper presents a systematic approach to
deriving energy conserving schemes for frictionless impact modelling. The
proposed numerical formulations follow from discretising Hamilton's equations
of motion, generally leading to an implicit system of nonlinear equations that
can be solved with Newton's method. The approach is first outlined for point
mass collisions and then extended to distributed settings, such as vibrating
strings and beams colliding with rigid obstacles. Stability and other relevant
properties of the proposed approach are discussed and further demonstrated with
simulation examples. The methodology is exemplified through a case study on
tanpura string vibration, with the results confirming the main findings of
previous studies on the role of the bridge in sound generation with this type
of string instrument
Specific "scientific" data structures, and their processing
Programming physicists use, as all programmers, arrays, lists, tuples,
records, etc., and this requires some change in their thought patterns while
converting their formulae into some code, since the "data structures" operated
upon, while elaborating some theory and its consequences, are rather: power
series and Pad\'e approximants, differential forms and other instances of
differential algebras, functionals (for the variational calculus), trajectories
(solutions of differential equations), Young diagrams and Feynman graphs, etc.
Such data is often used in a [semi-]numerical setting, not necessarily
"symbolic", appropriate for the computer algebra packages. Modules adapted to
such data may be "just libraries", but often they become specific, embedded
sub-languages, typically mapped into object-oriented frameworks, with
overloaded mathematical operations. Here we present a functional approach to
this philosophy. We show how the usage of Haskell datatypes and - fundamental
for our tutorial - the application of lazy evaluation makes it possible to
operate upon such data (in particular: the "infinite" sequences) in a natural
and comfortable manner.Comment: In Proceedings DSL 2011, arXiv:1109.032
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