Algebraic derivation
The above equivalent forms are readily verified by deriving the
transfer function from the striking-force input to the output
force signal
Referring to Fig.6.15, denote the input
hammer-strike transform by
and the output signal
transform by
. Also denote the loop-filter transfer function
by
. By inspection of the figure, we can write
![$\displaystyle F_o(z) = z^{-N} \left\{ F_i(z) + z^{-2M}\left[F_i(z) + z^{-N} H_l(z)F_o(z)\right]\right\}.
$](http://www.dsprelated.com/josimages_new/pasp/img1464.png)

The final factored form above corresponds to the final equivalent form shown in Fig.6.17.
Next Section:
Related Forms
Previous Section:
Computational Savings