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Embedded Systems

Physical Audio Signal Processing
    Acoustic Modeling with Digital Delay
       Comb Filters
          Feedback Comb Filters

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Feedback Comb Filters

The feedback comb filter uses feedback instead of a feedforward signal, as shown in Fig.1.18 (drawn in ``direct form 2'' [460]).

Figure 1.18: The feedback comb filter.
\begin{figure}\input fig/fbcf.pstex_t \end{figure}

A difference equation describing the feedback comb filter can be written in ``direct form 1'' [460] as2.5

$\displaystyle y(n) = b_0 x(n) - a_M y(n-M). $

The feedback comb filter is a special case of an Infinite Impulse Response (IIR) (``recursive'') digital filter, since there is feedback from the delayed output to the input [460]. The feedback comb filter can be regarded as a computational physical model of a series of echoes, exponentially decaying and uniformly spaced in time. For example, the special case

$\displaystyle y(n) = x(n) + g\, y(n-M) $

is a computational mod