scholarly journals Block-Based Physical Modeling with Applications in Musical Acoustics

2008 ◽  
Vol 18 (3) ◽  
pp. 295-305 ◽  
Author(s):  
Rudolf Rabenstein ◽  
Stefan Petrausch
Keyword(s):  
Discrete Time ◽  
Physical Modeling ◽  
Digital Filters ◽  
General Idea ◽  
Physical Systems ◽  
Wave Variables ◽  
Musical Acoustics ◽  
Starting Point ◽  
Block Based ◽  
Modeling Physical Systems

Block-Based Physical Modeling with Applications in Musical AcousticsBlock-based physical modeling is a methodology for modeling physical systems with different subsystems. Each subsystem may be modeled according to a different paradigm. Connecting systems of diverse nature in the discrete-time domain requires a unified interconnection strategy. Such a strategy is provided by the well-known wave digital principle, which had been introduced initially for the design of digital filters. It serves as a starting point for the more general idea of block-based physical modeling, where arbitrary discrete-time state space representations can communicate via wave variables. An example in musical acoustics shows the application of block-based modeling to multidimensional physical systems.

Digital Filters

2011 ◽  
pp. 180-196
Author(s):  
Gordana Jovanovic-Dolecek
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Digital Filters ◽  
Time Signal ◽  
Digital Signals ◽  
Video Signals ◽  
Time Signals ◽  
Time Distance ◽  
Independent Variable ◽  
Distance Position

A signal is defined as any physical quantity that varies with changes of one or more independent variables, and each can be any physical value, such as time, distance, position, temperature, or pressure (Oppenheim & Schafer, 1999; Elali, 2003; Smith, 2002). The independent variable is usually referred to as “time”. Examples of signals that we frequently encounter are speech, music, picture, and video signals. If the independent variable is continuous, the signal is called continuous-time signal or analog signal, and is mathematically denoted as x(t). For discrete-time signals the independent variable is a discrete variable and therefore a discrete-time signal is defined as a function of an independent variable n, where n is an integer. Consequently, x(n) represents a sequence of values, some of which can be zeros, for each value of integer n. The discrete–time signal is not defined at instants between integers and is incorrect to say that x(n) is zero at times between integers. The amplitude of both the continuous and discrete-time signals may be continuous or discrete. Digital signals are discrete-time signals for which the amplitude is discrete. Figure 1 illustrates the analog and the discrete-time signals.

Ocean ecosystem discrete time dynamics generated by ℓ-Volterra operators

2019 ◽  
Vol 12 (02) ◽  
pp. 1950015 ◽  
Author(s):  
U. A. Rozikov ◽  
S. K. Shoyimardonov
Keyword(s):  
Dynamical System ◽  
Fixed Points ◽  
Discrete Time ◽  
Volterra Operator ◽  
Saddle Points ◽  
Time Dynamics ◽  
Discrete Time Dynamical System ◽  
Starting Point ◽  
Ocean Ecosystem ◽  
Initial Starting

We consider a discrete-time dynamical system generated by a nonlinear operator (with four real parameters [Formula: see text]) of ocean ecosystem. We find conditions on the parameters under which the operator is reduced to a [Formula: see text]-Volterra quadratic stochastic operator mapping two-dimensional simplex to itself. We show that if [Formula: see text], then (under some conditions on [Formula: see text]) this [Formula: see text]-Volterra operator may have up to three or a countable set of fixed points; if [Formula: see text], then the operator has up to three fixed points. Depending on the parameters, the fixed points may be attracting, repelling or saddle points. The limit behaviors of trajectories of the dynamical system are studied. It is shown that independently on values of parameters and on initial (starting) point, all trajectories converge. Thus, the operator (dynamical system) is regular. We give some biological interpretations of our results.

Simple random walk statistics. Part I: Discrete time results

1996 ◽  
Vol 33 (2) ◽  
pp. 311-330 ◽  
Author(s):  
W. Katzenbeisser ◽  
W. Panny
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Order Statistics ◽  
Discrete Time ◽  
Rank Order ◽  
Simple Random Walk ◽  
Alternative Method ◽  
Starting Point ◽  
Famous Paper ◽  
Rank Order Statistics

In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.

scholarly journals Large-Scale Physical Modeling Synthesis, Parallel Computing, and Musical Experimentation: The NESS Project in Practice

2020 ◽  
Vol 43 (2-3) ◽  
pp. 31-47 ◽  
Author(s):  
Stefan Bilbao ◽  
James Perry ◽  
Paul Graham ◽  
Alan Gray ◽  
Kostas Kavoussanakis ◽  
...  
Keyword(s):  
Physical Modeling ◽  
Large Scale ◽  
Algorithm Design ◽  
Musical Instruments ◽  
Synthesis System ◽  
Professional Musicians ◽  
Musical Acoustics ◽  
Modeling Systems ◽  
Computational Resources ◽  
Theoretical Developments

Sound synthesis using physical modeling, emulating systems of a complexity approaching and even exceeding that of real-world acoustic musical instruments, is becoming possible, thanks to recent theoretical developments in musical acoustics and algorithm design. Severe practical difficulties remain, both at the level of the raw computational resources required, and at the level of user control. An approach to the first difficulty is through the use of large-scale parallelization, and results for a variety of physical modeling systems are presented here. Any progress with regard to the second difficulty requires, necessarily, the experience and advice of professional musicians. A basic interface to a parallelized large-scale physical modeling synthesis system is presented here, accompanied by first-hand descriptions of the working methods of five composers, each of whom generated complete multichannel pieces using the system.

Sign in / Sign up

Export Citation Format

Share Document