The development of algorithms for FFT processing of sparse data

Concerns a PC-based sonar system developed as an instructional aid in the teaching of signal processing, radar systems engineering and software engineering by means of project work. The aim is that the equipment will be multifunctional and capable of being configured to demonstrate such techniques as pulse, pulsed doppler, MTI, pulse compression, synthetic aperture and phased array radars. A phased array sonar system which employs a broad beam width transmitter and an array of 8 ultrasonic receiver transducers has been constructed. The angle of arrival of target reflections is found by calculating the Fourier transform of the samples taken across the elements of the array. Since the input data is sparse, 8 complex samples are used to determine 256 possible angles of arrival, a 256×256 FFT would be inefficient. An efficient algorithm based on the decimation-in-frequency FFT has been derived using McWhirter´s algorithmic engineering method (1992) augmented with the notation used in Jones´s Vienna development method (1989). The resultant algorithm is compared with Markel´s method (1971) based on pruning the paths associated with the zero inputs from the flow diagram of a decimation-in-time FFT