> I'm planning to do all of the beam forming digitally as well. You
> mentioned an
> analog multiplexer. I had assumed that all of the ADC samples
> need to be taken
> simultaneously. How necessary is that?

First, you get ignore the delay with some error, especially if it is very
fast compare to your
signal. Second, you can compensate for this delay when you form the beam
using predefined delays. You definitely don't want to have an A/D for each
hydrophone, this will be too painful.

>
> I understand the beamforming principles right up to the part
> about predefined
> weights. How do I determine the weights? I've also seen mention
> of "null" beams.
> What are they?

You can use a computer simulation and play with the weights. The more
accurate information you will have on the individual hydrophones, the more
accurate the simulation will be.

For a starter, try a simple simulation where you assume perfect, omni
directional individual hydrophones. Assume a target at direction (angle) P,
compute the relative phase of each of the signals (consider relative delays
in the water and your own beam forming delays and then convert the relative
delay to signal phase of your specific signal frequency). Then sum all the
signals using the phases you found and the weight combination you want to
try. When you sum the signals, pick the first two, find the combined phase
and amplitude, then add the third, and so on. This will give you to total
signal level from that direction. Then iterate on angle P and find the
signal level in each direction. This will allow you to draw the beam
diagram.

The basic math here is adding two sinus signals in amplitude A1, A2 and
phases (angles) B1, B2. This will give you the amplitude (A3) and phase (B3)
of the combined signal.

   A1*Sin(W + B1) + A2 x Sin(W + B2) =  A3*Sin(W + B3).

Anybody remembers the formula to find A3, B3 ?

I used to do these simulations long time ago in Basic using a teletype and a
punch tape. This days I would consider using it in Excel.

Tal

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