Convergence conditions for multi-channel free-field sound cancelling systems

The paper considers the convergence robustness of large channel number active noise control systems, for free-field sound cancellation. The approach uses a technique of directional active noise control (Electronically Controlled Acoustic Shadows). The system produces quiet regions in the form of deep sharp shadows, confined within control angles, extending out to large distances from the unwanted source of noise. The cancelling system has intelligence in which it can absorb selectively the unwanted sound and leave other wanted sounds unchanged. It has the potential to out perform conventional classical sound blocking systems, with the ability to generate the perfect shadow, without acoustic leakage (diffraction). It is found that the cancelling system has a series of instability spectral peaks corresponding to propagation path differences between the secondary sources and detection microphones of multiples of acoustic half wavelengths of the source frequency. These peaks need to be avoided to produce a robust convergent system.