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A reduced ROM-based architecture blending the concepts of domain folding and angle recoding to implement the coordinate rotation digital computer (CORDIC) algorithm is proposed. Domain folding restricts the domain of the sine/cosine functions in [0, pi/8] instead of [0, 2pi]. The addition identities of the trigonometric functions are adopted to determine the range of sine/cosine functions mapped from the domain [0, pi/4] based on that restricted in the domain [0, pi/8]. The quarter-wave symmetry property is then applied to obtain the range mapped from the full domain [0, 2pi]. Applying the angle recoding process to the angle in the domain [0, pi/8] affords two benefits. One is a reduction of about 50% in the size of the ROM lookup table storing the information of the coarse angles, except for the fact that the number of stages (N) equals 3k+2 where k is an integer; the other benefit is a 1-bit improvement in the precision in the CORDIC implementation.
Date of Publication: June 2008