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Beamforming **Previous:** Basic Idea **Contents**

What kind of results can we expect from a delay-and-sum beamformer?
For now we'll assume that the source angle is known and we can
delay the signals without any error. First some definitions:

Now put into the average power
definition. Then,

If we delay so that
, then we get
.
Repeat the above procedure with the noise and expand.

The time-averaged cross-correlation,
, is zero for noise.
Then,
.
And

And in general, for M microphones, we get M times the SNR [MIK]. For the Signal to Interference Ratio
(SIR), the cross-correlation term will take a value between zero
and the interference power. So the array SIR will be better than
the one element microphone SIR and worse than M times the SIR for
one microphone.

**Next:** Finding the Delay **Up:** Delay-and-Sum
Beamforming **Previous:** Basic Idea **Contents**
Todd A Goldfinger 2004-11-22