Example Tapped Delay Line

An example of a TDL with two internal taps is shown in Fig. 1.13. The total delay line length is $M_3$ samples, and the internal taps are located at delays of $M_1$ and $M_2$ samples, respectively. The output signal is a linear combination of the input signal $x(n)$, the delay-line output $x(n-M_3)$, and the two tap signals $x(n-M_1)$ and $x(n-M_2)$.

Figure 1.13: Tapped Delay Line (TDL).

The difference equation of the TDL in Fig. 1.13 is, by inspection,

$$y(n) = b_0 x(n) + b_{M_1} x(n-M_1) + b_{M_2} x(n-M_2) + b_{M_3} x(n-M_3)$$

corresponding to the transfer function

$$H(z) = b_0 + b_{M_1} z^{-M_1} + b_{M_2} z^{-M_2} + b_{M_3} z^{-M_3}$$