Radar mapping: Prolate spheroidal wave functions versus truncated inverse fourier transform

Prolate spheroidal wave functions may be used to obtain an estimate of a distributed source that has been observed from an aperture of finite size. An estimate of the source distribution can also be obtained by the use of the truncated inverse Fourier transform. A quantitative measure is obtained of the reductions in the mean-squared error in the estimates which are produced by the data processing techniques. The relative merits of the two processing techniques depend upon the aperture size and the signal-to-noise ratio. The processing of data by means of the wave functions is found to be more advantageous for small apertures and for large signal-to-noise ratios. The processing techniques are also compared as to the ability to reconstruct the detail in an isolated target or source distribution of limited size. The wave functions are shown to be useful for the processing of data obtained from a large aperture that is used to observe a small target.