The Problem of Calculating the Fast-Fourier Transform of a Step-Like Sampled Function

A method to increase the accuracy of fast Fourier transform calculations for rapidly varying functions

“…In a first step, calculations of its transform have been per formed by Nicolson's method [2] or the steep-ramp method [3] with an improved corrective term (cf. footnote 1), the re sults of which are of comparable accuracy.…”

“…1, the part of the waveform in the crosshatched regions are truncated. To take this truncation into account, some authors [2], [3] have proposed to subtract a known function from the initial points before transformation, and then compensating for this subtraction by a corrective term added after transformation. 1 In this case, the subtracted function was only connected to the calculation interval rather than to the function to be transformed.…”

“…As regards the steep-ramp method proposed by this author [3], the cor rective terms obtained from a continuous complementary ramp may be im proved by sampling this ramp, according to Fig. 1 or [3, fig.…”