FIR Digital Filters in a Linear Array Processor

Details of frequency domain beamforming for the processing of a broadband sonar frequency signal from a linear array are presented. The case of a frequency resolution of about 0.025 Hz is employed as an example. The input sampling rate is determined to span the frequency broadband of interest. This is followed by an inphase and quadrature approach to shift a chosen 5 Hz band to the baseband. A cascade of three FIR digital filters then achieves a passband of 2.5 Hz and an attenuation of 80 dB with a transition band of 8.01 Hz, necessary to prevent aliasing into the passband from an output sampling rate of 13.01 Hz. A cascade configuration of digital filters and interstage decimation lead to a reduction in the output multiplication rate. The design of individual filters was arrived at by employing the approach of Farden and Scharf. An alternate and conceptually transparent derivation of the design principle by the classical weighted minimum mean squared error method is presented.