In [56] Candy locates the beginning of the classical period of spectral estimation in Schuster s use of Fourier techniques in 1898 to analyze sun-spot data [170]. The role of Fourier techniques grew with the discovery, by Wiener in the USA and Khintchine in the USSR, of the relation between the power spectrum and the autocorrelation function. Much of Wiener s important work on control and communication remained classified and became known only with the publication of his classic text Time Series in 1949 [189]. The book by Blackman and Tukey, Measurement of Power Spectra [16], provides perhaps the best description of the classical methods. With the discovery of the FFT by Cooley and Tukey in 1965, all the pieces were in place for the rapid development of this DFT-based approach to spectral estimation.

Until about the middle of the 1970s most signal processing depended almost exclusively on the DFT, as implemented using the FFT. Algorithms such as the Gerchberg-Papoulis bandlimited extrapolation method were performed as iterative operations on finite vectors, using the FFT at every step. Linear filters and related windowing methods involving the FFT were also used to enhance the resolution of the reconstructed objects. The proper design of these filters was an area of interest to quite a number of researchers, John Tukey among them. Then, around the end of that decade, interest...