Methods and apparatus for signal processing are disclosed. A discrete time domain input signal xm(t) may be produced from an array of microphones M0 . . . MM. A listening direction may be determined for the microphone array. The listening direction is used in a semi-blind source separation to select the finite impulse response filter coefficients b0, b1 . . . , bN to separate out different sound sources from input signal xm(t). One or more fractional delays may optionally be applied to selected input signals xm(t) other than an input signal x0(t) from a reference microphone M0. Each fractional delay may be selected to optimize a signal to noise ratio of a discrete time domain output signal y(t) from the microphone array. The fractional delays may be selected to such that a signal from the reference microphone M0 is first in time relative to signals from the other microphone(s) of the array. A fractional time delay Δ may optionally be introduced into an output signal y(t) so that: y(t+Δ)=x(t+Δ)*b0+x(t−1+Δ)*b1+x(t−2+Δ)*b2+ . . . +x(t−N+Δ)bN, where Δ is between zero and ±1.