Frequency-domain separation of convolved non-stationary signals with adaptive non-causal FIR filters

In the frequency domain, a convolutive signal separation problem can be decomposed into multiple instantaneous separation problems that can be solved independently by an instantaneous separation algorithm. In this case, however, permutation indeterminacy in each frequency bin is a crucial problem. To solve this problem, a constrained gradient method has been suggested recently. In this paper, we propose an alternative procedure that realizes the same constrained gradient method with reduced computation. To invert a non-minimum phase system, non-causal finite impulse response (FIR) filters are employed in our realization. In addition, we derive a new instantaneous separation algorithm by minimizing the Hadamard inequality criterion with the natural gradient method. The algorithm has the equivariant property for uniform performance and belongs to orthogonal learning algorithms by nature. An improved separation was achieved for real-world speech-speech signals.