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Feedback Comb Filter


\epsfig{file=eps/fbcf.eps,width=\textwidth }


\begin{eqnarray*}
-a_M &=& \hbox{Feedback coefficient (need $\vert a_M\vert<1$\ for stability)}\\
M &=& \hbox{Delay-line length in samples}
\end{eqnarray*}

Direct-Form-II Difference Equation (see figure):

\begin{eqnarray*}
v(n) &=& x(n) - a_M \,v(n-M)\\
y(n) &=& b_0\, v(n)
\end{eqnarray*}

Direct-Form-I Difference Equation
(commute gain $ b_0$ to the input):

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

Transfer Function

$\displaystyle H(z) = \frac{b_0}{1 + a_M z^{-M}}
$

Frequency Response

$\displaystyle H(e^{j\omega T}) = \frac{b_0}{1 + a_M e^{-jM\omega T}}
$


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Download Delay.pdf
Download Delay_2up.pdf
Download Delay_4up.pdf

``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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