To handle the high bandwidth and large number of elements needed for high resolution sonar, the necessary sampling rate is quite large. Large amounts of memory are also required to handle the long delays associated with large arrays and high sample rates. Because of the high implementation cost, digital interpolation beamformers are generally used instead. Now we sample at just above the Nyquist rate, and achieve the desired time-delay resolution by digital interpolation of the sampled data. In the above digital system, the sensors are sampled at the interval D , needed to satisfy the Nyquist criterion.
L is an integer larger than one.
Beam degradation introduced by interpolation is controllable and quite small for an interpolation filter of modest design. Since the filter and the summation are both linear, the filter can be placed either before or after the beamformer summation. Since FIR filters are not ideal, error is introduced at the beamformer output. Increasing the number of filter coefficients reduces this error, so there is a tradeoff between accuracy and computational complexity. Again, frequency-domain beamforming is inherently narrowband.