Handbook of Signal Processing Systems by Shuvra S. Bhattacharyya & Ed F. Deprettere & Rainer Leupers & Jarmo Takala

Author:Shuvra S. Bhattacharyya & Ed F. Deprettere & Rainer Leupers & Jarmo Takala
Language: eng
Format: epub
ISBN: 9783319917344
Publisher: Springer International Publishing

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where and . This requires three real-valued multiplications and three real-valued additions as shown in Fig. 7c. The other three standard alternatives have a similar form, but differ in how the coefficient corresponding to D is derived. Based on the angle, a structure can be selected to make sure that . This avoids the large magnitudes obtained for certain angles, as in the example structure D →∞ when α → π.

3.2.2 Multi-Stage General Rotators

As opposed to the multiplier-based rotators in the previous section, multi-stage rotators perform only a part of the total rotation in each stage. Step k of such a rotator can rotate with a set of angles, typically δ k α k, where δ k ∈{−1, 1} or δ k ∈{−1, 0, 1}, i.e., a fixed angle, α k, can be rotated in either direction or rotated in either direction or no rotation at all. Based on the remaining angle to be rotated, z k, δ k is determined and the remaining angle after the rotation, z k+1, is updated.

The general structure of a rotation stage includes the calculation of x k+1, y k+1 and z k+1 and is shown in Fig. 8. Multi-stage rotators mainly involve the CORDIC algorithm and its variations.

Fig. 8General rotation stage in multi-stage rotator

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