Feedback delay

Figure 3.22 Stautner and Puckette s four channel feedback delay network [Stautner and Puckette, 1982],...

Figure 3.23 Feedback delay network as a general specification of a reverberator containing Y delays [Jot and Chaigne, 1991]...

Rocchesso and Smith, 1994] Rocchesso, D. and Smith, J. O. (1994). Circulant feedback delay networks for sound synthesis and processing . In Proc. Int. Computer Music Conf, pages 378-381. 

Stautner and Puckette s four channel feedback delay network 118... 

Feedback delay network as a general specification of a reverberator... 

Now we discuss algorithms that reproduce late reverberation. The material is presented in roughly chronological order, starting with reverberators based on comb and allpass filters, and proceeding to more general methods based on feedback delay networks. 

Jot generalizes the notion of a monophonic reverberator using the feedback delay network (FDN) structure shown in figure 3.23. The structure is a completely general specification of a linear system containing N delays. 

This is verified to be identical to equation 3.21. Any series combination of elementary filters - for instance, a series allpass filter - can be expressed as a feedback delay network with a triangular feedback matrix [Jot and Chaigne, 1991],... 

This measure can be used to characterize the various forms of frequency locking between the two modes. With varying feedback delay T and varying slope a of the open loop feedback curve, Fig. 12.11 shows how the two oscillatory modes can adjust their dynamics and attain states with different rational relations (p q) between... 

A clear benefit of the coupled approach, in contrast to integration, is the flexibility in the choice of different coupled chemical schemes represented by the different CTMs. However, the required 3D coupling is less consistent than an integrated system because of feedback delay and dislocation due to different transport representations (see Sect. 10.2.4) in the IFS and the CTM. 

Foulkes, A. J. and MiaU, R. C. 2000. Adaptation to visual feedback delays in a human manual tracking task. Exp. Brain Res. 131 101-110. 

Control actions will generally lag in their effects on the process because of delays in signal propagation around the control loop an actuator may not respond immediately to an external command signal (called dead time) the process may have delays in responding to manipulated variables (time constants) and the sensors may obtain values only at certain sampling intervals (feedback delays), lime lags restrict the speed and extent with which the effects of disturbances, both within the process itself and externally derived, can be reduced. They also impose extra requirements on the controller, for example, the need to infer delays that are not directly observable. 

Delays may not be directly observable, but may need to be inferred. Depending on where in the feedback loop the delay occurs, different control algorithms are required to cope with the delays [25] dead time and time constants require an algorithm that makes it possible to predict when an action is needed before the need. Feedback delays generate requirements to predict when a prior control action has taken effect and when resources will be available again. Such requirements may impose the need for some type of open loop or feedforward strategy to cope with... 

In summary, both the design of the communication channels and the communication dynamics must be considered as well as potential feedback delays. As an example of communication dynamics, reliance on face-to-face verbal reports during group meetings is a common method of assessing lower-level operations [189], but, particularly when subordinates are communicating with superiors, there is a tendency for adverse situations to be underemphasized [20]. 

The cybernetic description of systems of different types is characterized by concepts and definitions like feedback, delay time, stochastic processes, and stability. These aspects will, for the time being, be demonstrated on the control loop as an example of a simple cybernetic system, but one that contains all typical properties. Thereby the importance of the probability calculus and communication in cybernetics can be clearly explained. This is then followed by a general representation of cybernetic systems. 

---