 Microphone
Arrays.
We hope this will be a gentle introduction to microphone arrays. Let
us start with the simplest case - a dipole. Take two (ideal) perfectly
omnidirectional, flat-response, microphones, and put them at a certain
distance from each other.
Now imagine an ideal punctiform source s, emitting spherical vawes.
The sound from s will reach the two microphones with different time
delays. This difference d - which is the only one measurable
(observable) at the dipole location - is a (simple) function of the
differential path r and of the speed of sound.
Let us now apply a delay d on the signal coming from m1, then sum
this delayed signal with that coming from m2. In this way, you get just
(about) twice the signal coming from s, because you exactly compensated
the delay between the two incoming signals. This is not the case for the
signal coming from another generic source s', whose two incoming signals
have a different differential path, and, as a consequence, a different
relative delay. In this case, the sum will give:
signal(t) = fs'(t)+fs'(t+t')
where t' is the difference between the delay applied (taken from r,
the desired differential path) and the delay due to the differential
path of s'. This delayed sum (a linear operation) is equivalent to the
application of a periodic comb filter.
Of course, s is not the only point in space having that special delay
relationship. Any point lying over a hyperboloid trough s, that has its
focus at the mid-point between the two microphones, will have the
same delay relationship. The delay-and-sum operation will thus leave
intact the signal coming from these points.
Thus a dipole can discriminate between points in space, leaving
intact those lying on a surface, and applying a comb filter to the
others. This kind of filter attenuates, of course, the energy of the
signal, but with the exception of the frequency components (partials)
lying near the filter peaks. Thus a dipole has just a weak spatial
selectivity.
But it is easy to understand that by combining more dipoles, things
will go better. If you use three orthogonal dipoles - i.e., four
microphones (not six), one being in common between the dipoles - the
locus of the points focused will be the intersection (if existent) of
three hyperboloids, i.e. just a single point. More, the comb filters
applied at the other points will be, in general, different for each
dipole, so they will interact destructively
As easily seen, all those things are controlled by the delays applied
to the various microphones. Controlling these delays is very
straightforward using DSP. The position of the focused point can thus be
fully electronically controlled.
If you need further information about this subject, please go to this
page.
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