Transfer Function Models for Multidimensional Systems with Bounded spatial Domains

Abstract

Multidimensional (MD) systems describe relations between signals depending on two or more independent variables. They are also called distributed parameter systems, if the independent variables are time and space. The only conventional models for their description are partial differential equations. This is in contrast to onedimensional (lumped parameter) systems, where a variety of different models including transfer functions is used. This paper extends the concept of transfer function models to multidimensional systems with bounded spatial domains, i.e., systems which can be described as initialboundary-value problems. These transfer function models are useful for system analysis and as a starting point for the derivation of numerically efficient discrete simulation models.

The Use of Low-Frequency Ultrasonics in Speech Processing

“…Since � � �� � � � �������, we need to take the inverse SL transform (Rabenstein, 1999) to reach ����.…”

“…In our approach to derive a linear model, in this section the VT transfer function is determined using the functional transformation method (FTM) which converts the linear PDEs to algebraic equations including boundary and initial conditions, similarly to Laplace transformation in ordinary PDEs (Rabenstein, 1999).…”

“…Next we seek another transform � which can convert the spatial differential operator � � to algebraic equations. Lacking a general transform similar to the Laplace transform in the spatial domain, the spatial Sturm-Liouville transform (SLT) (Rabenstein, 1999) is applied:…”

“…Values of ���� � � �� � � are Eigen functions and Eigen values of the operator � � � � � (Rabenstein, 1999). We then substitute the results in (33):…”

Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

“…in the control system synthesis. In contrast, analytical methods allow for more thorough physical interpretation of the process and are more useful in the automatic control theory [20].…”