Reflectively Terminated Waveguide Filters

A reflecting termination occurs when the wave impedance of the next section is either zero or infinity (§C.8.1). Since Fig.C.24 is labeled for force waves, an infinite terminating impedance on the right results in

Similarly, a zero terminating impedance on the right gives

For velocity waves, the signs are interchanged. Thus, a reflectively terminated ladder digital waveguide corresponds to a final feedback with gain at the end of the ladder. Such a termination will be used below to derive conventional ladder/lattice filters below.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.