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Example Tapped Delay Line

An example of a TDL with two internal taps is shown in Fig.2.19. 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 2.19: Tapped Delay Line (TDL).
\includegraphics{eps/tdl}

The difference equation of the TDL in Fig.2.19 is, by inspection,

$\displaystyle 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

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


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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