Tapped Delay Line (TDL)A tapped delay line (TDL) is a delay line with at least one ``tap''. A delay-line tap extracts a signal output from somewhere within the delay line, optionally scales it, and usually sums with other taps for form an output signal. A tap may be interpolating or non-interpolating. A non-interpolating tap extracts the signal at some fixed integer delay relative to the input. Thus, a tap implements a shorter delay line within a larger one, as shown in Fig.2.18.
Example Tapped Delay LineAn example of a TDL with two internal taps is shown in Fig.2.19. The total delay line length is samples, and the internal taps are located at delays of and samples, respectively. The output signal is a linear combination of the input signal , the delay-line output , and the two tap signals and . difference equation of the TDL in Fig.2.19 is, by inspection,
Transposed Tapped Delay Line
TDL for Parallel ProcessingWhen multiplies and additions can be performed in parallel, the computational complexity of a tapped delay line is multiplies and additions, where is the number of taps. This computational complexity is achieved by arranging the additions into a binary tree, as shown in Fig.2.21 for the case .
General Causal FIR FiltersThe most general case--a TDL having a tap after every delay element--is the general causal Finite Impulse Response (FIR) filter, shown in Fig.2.22. It is restricted to be causal because the output may not depend on ``future'' inputs , , etc. The FIR filter is also called a transversal filter. FIR filters are described in greater detail in . difference equation for the th-order FIR filter in Fig.2.22 is, by inspection,