Transposed Tapped Delay Line

Figure 1.14: Transposed Tapped Delay Line (TTDL).

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 [312, 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 [312].