Feedback Comb Filters
The feedback comb filter uses feedback instead of a feedforward signal, as shown in Fig.2.24 (drawn in ``direct form 2'' [449]).
A difference equation describing the feedback comb filter can be written in ``direct form 1'' [449] as3.9
![$\displaystyle y(n) = b_0 x(n) - a_M y(n-M).
$](http://www.dsprelated.com/josimages_new/pasp/img493.png)
![$\displaystyle y(n) = x(n) + g\, y(n-M)
$](http://www.dsprelated.com/josimages_new/pasp/img494.png)
![$ g$](http://www.dsprelated.com/josimages_new/pasp/img37.png)
For stability, the feedback coefficient must be less than
in magnitude, i.e.,
. Otherwise, if
,
each echo will be louder than the previous echo, producing a
never-ending, growing series of echoes.
Sometimes the output signal is taken from the end of the delay line instead of the beginning, in which case the difference equation becomes
![$\displaystyle y(n) = b_M x(n-M) - a_M y(n-M) .
$](http://www.dsprelated.com/josimages_new/pasp/img498.png)
![$ M$](http://www.dsprelated.com/josimages_new/pasp/img11.png)
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Feedforward Comb Filter Amplitude Response
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Feedforward Comb Filters