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Beamforming Previous: Finding the 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.
Todd A Goldfinger 2004-11-22