Wave Digital Filters

In this section, we discuss the basic concepts and strategies for using wave digital filtering techniques. For a more detailed and complete discussion, see the following wave digital filter link.

Background

General Approach

A WDF model of a system can be developed from its continuous-time, differential equation representation as follows:

  1. Express all physical quantities, such as forces and velocities, in terms of traveling-wave components.

  2. Digitize the resulting traveling-wave system using the bilinear transform.

  3. Combine elementary components (mass, springs, ...) using scattering junctions defined by either series or parallel connections.

A ``Physical'' Derivation

Fundamental WDF Elements

  1. From the previous discussion, a WDF mass element has R0 = m and a digitized reflectance given by

    Sm(z) = -z-1.

  2. In a similar way, the discrete-time reflectance for a WDF spring with R0 = k is found to be

    Sk(z) = z-1.

  3. A WDF dashpot (or resistance) is defined to have $R_0 = \mu$ and a reflectance

    \begin{displaymath}
S_{\mu}(z) = 0.
\end{displaymath}

Connecting Wave Digital Elements

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