Apparatus and method for generating a sequence of sines or cosin

Details Apparatus and method for generating a sequence of sines or cosin Apparatus and method for generating a sequence of sines or cosin

1988-06-22

1989-10-31

Harkcom, Gary V.

Boots, shoes, and leggings

G06F 102

Patent

active

048781878

ABSTRACT:
A data bank consisting of two tables of length log.sub.2 N 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./2.sup.N. ) 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.

REFERENCES:
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patent: 4584658 (1986-04-01), Ottobre et al.
patent: 4718030 (1988-01-01), Tsutsumi
Tierney et al, "A Digital Frequency Synthesizer", IEEE Trans. on Audio and Electroacoustics, vol. AU-19, No. 1, 3/71, pp. 48-56.
Baker, "Suggestion for a Fast Binary Sine/Cosine Generator", IEEE Trans. on Computer, Nov. 1976, pp. 1134-1136.
Buneman, "Conversion of FFT's to Fast Hartley Transforms", SIAMJ. Sci. Stat. Comp., vol. 7, No. 2, pp. 624-638, 1986.
C. Oliver, "Stable Methods for Evaluating the Points cos (i.pi./.eta.)", J. Inst. Maths. Applic., vol. 16, pp. 247-257, 1975.

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