Equivalence of Parallel Combs to TDLs
It is easy to show that the TDL of Fig.2.19 is equivalent to a
parallel combination of three feedforward comb filters, each as in
Fig.2.23. To see this, we simply add the three comb-filter transfer
functions of Eq.(2.3) and equate coefficients:
![\begin{eqnarray*}
H(z) &=& \left(1+g_1 z^{-M_1}\right) +
\left(1+g_2 z^{-M_2}\...
...\right) \\
&=& 3 + g_1 z^{-M_1} + g_2 z^{-M_2} + g_3 z^{-M_3}
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/pasp/img523.png)
which implies
![$\displaystyle b_0 = 3,\; b_{M_1} = g_1,\; b_{M_2} = g_2,\; b_{M_3} = g_3 .
$](http://www.dsprelated.com/josimages_new/pasp/img524.png)
We see that parallel comb filters require more delay memory
(
elements) than the corresponding TDL, which only
requires
elements.
Next Section:
Equivalence of Series Combs to TDLs
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Filtered-Feedback Comb Filters