This paper proposes a new way of tidal spectral analysis based on the Cooley-Tukey algorithm, known as the Fast Fourier Transform. The Fast Fourier Transform analysis is used to compute both the harmonic constants of the tide and the power spectrum.The latter is obtained by means of a weighted sum. A new way is also derived to obtain the formula giving the number of the degrees of freedom,on which is based the confi dence interval corresponding to the noise spectrum.
A technique is described for the rapid Fourier transform of large series of numbers. The technique takes advantage of the fact that most digital series are highly factorizable by the number 2, which permits the use of the F.F.T. algorithm. Using two magnetic tape units, or alternatively magnetic disk facilities, very large series can be transformed efficiently with only modest computer facilities. For the transformation of odd-valued series the Thomas Prime-Factor and Gentleman and Sande algorithms are treated in detail.
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