Fractional Delay

The last thing we need to do is delay the signals and sum. If the delay falls on integer samples, this is simple enough. But because of the short distance between microphones, a delay filter with subsample accuracy is necessary. I have chosen the method of [Fa] to implement fractional delays. This method designs a fractional delay filter by letting the desired filter have coefficients that are a polynomial function. The polynomials are solved for by minimizing the distance between the desired filter and the theoretical unit gain optimal delay. This results in a delay filter that is very accurate over low frequencies but blows up for frequencies near the nyquist rate. Fortunately, most of the energy in speech is in the first few thousand hertz, and we can just ignore what happens at the higher frequencies without noticeable loss of quality.