| 摘要 |
A data bank consisting of two tables of length log2N suffices for the on-line creation of trigonometric functions of N successive angles, with only one addition and one multiplication per step. The data bank consists of some read only memory elements containing the half-secants of the angles delta , 2 delta , 4 delta , 8 delta , . . . where delta is the spacing of the successive angles. (In Fourier transforms, one needs a delta of the form pi /2N. ) The other half of the data bank is a random access memory of the same length as the ROM and is initially loaded with the trigonometric functions of that same set of angles. Mid-point interpolation based on values stored in the two tables is used to maintain entries necessary for successive angles. The second table begins, for instance, as a table of sines of the angles 2 pi , pi , pi /2, pi /4, pi /8, etc., but whenever an entry has been used, it is replaced by a new entry, calculated by mid-point interpolation and to be used in a later step.
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