As well as being able to reproduce sound in one region of space, it would be useful to reduce the level of reproduced sound in other spatial regions, with a “personal audio” system. For mobile devices this is motivated by issues of privacy for the user and the need to reduce annoyance for other people nearby. Such personal audio systems can be realized with arrays of loudspeakers that become superdirectional at low frequencies, when the array dimensions are small compared with the acoustic wavelength. The design of the array then becomes a compromise between performance and array effort, defined as the sum of mean squared driving signals. Various methods of formulating this tradeoff as a regularization problem have been suggested and the connection between these formulations is discussed. Large array efforts are due to strongly self-cancelling multipole arrays. A concern is then the robustness of such an array to variations in the acoustic environment and driver sensitivity and position. The design of an array that is robust to these uncertainties then leads to a generalization of regularization.

Timing and area of circuits are two of the most important design criteria to be optimized in data path synthesis. In addition, carry-save-adder (CSA) has been proven to be one of the most efficient implementation units in optimizing timing and/or area of arithmetic circuits. However, the existing approaches are restricted in using CSAs, i.e., optimizing operation trees separately without any interaction between them, resulting in a locally optimized CSA circuit. To overcome this limitation, we propose a practically efficient solution to the problem of an accurate exploration of timing and area trade-offs in optimizing arithmetic circuits in the presence of multiple operation trees using CSAs. The application of our approach is able to find a best CSA implementation of circuit in terms of timing and area.