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Embedded SystemsFPGAElectronics

Physical Audio Signal Processing
    Acoustic Modeling with Digital Delay
       Tapped Delay Line (TDL)
          Example Tapped Delay Line


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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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About the Author: 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.


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