Transposed Tapped Delay Line

In many applications, the transpose of a tapped delay line is desired, as shown in Fig.1.14, which is the transpose of the tapped delay line shown in Fig.1.13. A transposed TDL is obtained from a normal TDL by formal transposition of the system diagram. The transposition operation is also called flow-graph reversal [340, pp. 153-155]. A flow-graph is transposed by reversing all signal paths, which necessitates signal branchpoints becoming sums, and sums becoming branchpoints. For single-input, single-output systems, the transfer function is the same, but the input and output are interchanged. This ``flow-graph reversal theorem'' derives from Mason's gain formula for signal flow graphs. Transposition is used to convert direct-forms I and II of a digital filter to direct-forms III and IV, respectively [340].

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written by 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.