Delay Loop Expansion
When a subset of the resonating modes are nearly harmonically tuned, it can be much more computationally efficient to use a filtered delay loop (see §2.6.5) to generate an entire quasi-harmonic series of modes rather than using a biquad for each modal peak [439]. In this case, the resonator model becomes
![$\displaystyle H(z) \eqsp \sum_{k=1}^N \frac{a_k}{1 - H_k(z) z^{-N_k}},
$](http://www.dsprelated.com/josimages_new/pasp/img1794.png)
![$ N_k$](http://www.dsprelated.com/josimages_new/pasp/img1795.png)
![$ k$](http://www.dsprelated.com/josimages_new/pasp/img89.png)
![$ H_k(z)$](http://www.dsprelated.com/josimages_new/pasp/img1796.png)
![$ k$](http://www.dsprelated.com/josimages_new/pasp/img89.png)
Note that when is close to
instead of
, primarily
only odd harmonic resonances are produced, as has been used in
modeling the clarinet [431].
Next Section:
Measured Amplitude Response
Previous Section:
State Space Approach to Modal Expansions