Resonators

FDN's with short delay lines may be used to produce resonances irregularly spread over frequency. A possible application could be the simulation of resonances in the body or soundboard of a string instrument.

M. Mathews and J. Kohut [14] showed that, in this kind of simulation of the violin body, the exact position and height of resonances is not usually important; on the contrary, they stated that the Q's of the resonances must be sufficiently large and the peaks must be sufficiently close together. Thus, even in rather small physical resonators, a statistical matching may be as effective as a more precise, mode-for-mode matching.

With CFDNs we can easily achieve these goals, and we can vary the distribution of peaks by acting on the delay lengths and/or the feedback matrix. In this context, the main advantage of using CFDNs over general FDNs is that the feedback matrix has $N$ parameters which are related to the eigenvalues by means of a DFT. This means we have the possibility of controlling a large number of resonances using a number of parameters which is linear in the order of the structure, and the parameter control can be performed very efficiently and safely, i.e., without running into instabilities. The control over matrix eigenvalues is complementary with respect to the control of delay lengths: while changing a delay has a stretching or squeezing effect on resonance positions all along the frequency axis, changing the eigenvalues produces alternative changes in the distribution of resonances, such as clustering the peaks, as is illustrated in Fig. Fig. 3.

Another interesting application of CFDNs is as resonators in a feedback loop for pseudo-physical sound-synthesis techniques. By exciting these structures with bursts of white noise we obtain a multidimensional extension of the Karplus-Strong algorithm [11], that is very effective for simulating membranes and bars. Alternatively, we can couple these resonators with nonlinear exciters and explore new families of sustained sounds as in waveguide synthesis [29].

We have been using effectively CFDNs in live-electronic performances, where the exciting signal is coming from a traditional instrument, and the CFDN provides a complicated filtering pattern whose frequency shape can be controlled in real-time by its parameters (eigenvalues or row elements).