A Causality-Constrained Frequency-Domain Least-Squares Filter Design Method for Crosstalk Cancellation

Crosstalk cancellation filters play a crucial role when reproducing binaural signals over loudspeakers. Least-squares design methods for crosstalk cancellation filters are commonly formulated either in the time domain or in the frequency domain. While the time-domain problem is too complex to be solved in a dynamic real-time setup, the frequency-domain problem is computationally cheap. However, it yields circular convolution artifacts, which degrade the performance. Using a unified framework, we derive a causality-constrained frequency-domain least-squares problem, which itself is an unconstrained problem. Our method does not yield circular convolution artifacts since the impulse responses are causal by construction. This construction is based on the fact that the real part and the imaginary part of a causal signal's spectrum are related via Hilbert transform. By approximating the Hilbert transform, we reduce the proposed method's computational complexity. The complexity reduces by two to three orders of magnitude while the performance remains close to that of the time-domain solution. We provide a detailed complexity analysis and compare our method to three state-of-the-art methods on a large dataset. Our investigations reveal that the causality-constrained method enables a flexible tradeoff between computational complexity and performance figures.