A complex exponential algorithm developed for the representation and analysis of time-limited signals is defined, and its evaluation with respect to conventional discrete Fourier techniques is discussed. It is shown that for a given length of a signal containing discrete frequency information, sampled at least to the Nyquist criterion, the complex exponential algorithm can often provide increased frequency resolution over standard Fourier techniques. It is also shown that the complex exponential algorithm provides an improved mechanism over Fourier techniques for interpolation between points in a sampled signal containing discrete frequency components in the presence of broad-band noise. The effects of noise in the complex exponential technique and the computational difficulties associated with the present complex exponential algorithm are also discussed.
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Spitznogle et al. (1970) studied this question.