Pentomics, Inc.

Dengwei Fu

Alan Neil Willson, Jr

Arthur Torosyan

An angle rotator uses a coarse stage rotation and a fine stage rotation to rotate an input complex signal in the complex plane according to an angle &#x3b8;. The coarse stage rotation includes a memory device storing pre-computed cosine &#x3b8;and sine &#x3b8;values for fast retrieval, where &#x3b8;is a radian angle that corresponds to a most significant word (MSW) of the input angle &#x3b8;. The fine stage rotation uses one or more error values that compensate for approximations and quantization errors associated with the coarse stage rotation. The rotator consolidates operations into a small number of reduced-size multipliers, enabling efficient multiplier implementations such as Booth encoding, yielding a smaller and faster overall circuit.

Apparatus and method for angle rotation

A rectangular-to-polar-converter receives a complex input signal (having Xand Ycomponents) and determines an angle &#x3c6; that represents the position of the complex signal in the complex plane. The rectangular-to polar-converter determines a coarse angle &#x3c6;and a fine angle &#x3c6;, where &#x3c6;=&#x3c6;+&#x3c6;. The coarse angle &#x3c6;is obtained using a small arctangent table and a reciprocal table. These tables provide just enough precision such that the remaining fine angle &#x3c6;is small enough to approximately equal its tangent value. Therefore the fine angle &#x3c6;can be obtained without a look-up table, and the fine angle computations are consolidated into a few small multipliers, given a precision requirement. Applications of the rectangular-to-polar converter include symbol and carrier synchronization, including symbol synchronization for bursty transmissions of packet data systems. Other applications include any application requiring the rectangular-to-polar conversion of a complex input signal.

Apparatus and method for rectangular-to-polar conversion

A trigonometric interpolator interpolates between two data samples at an offset &mgr;, where the two data samples are part of a set of N data samples. The trigonometric interpolator fits a trigonometric polynomial to the N data samples and evaluates the trigonometric polynomial at the offset &mgr;. The trigonometric inteprolator can be utilized for data rate changing and to correct mismatches between received samples and transmitted symbols. Simulations demonstrate that the trigonometric interpolater attains better performance than &ldquo;conventional&rdquo; interpolators, while simultaneously reducing the required hardware. In embodiments, the filter response of the trigonometric interpolator can be modified to achieve an arbitrary frequency response in order to enhance the interpolator performance. More specifically, the frequency response of the interpolator can be shaped to effectively correspond with the frequency response of the input data samples and the offset &mgr;. Using this optimization technique, the overall interpolation error is reduced. As for the implementation, the optimal interpolator does not require additional hardware when a lookup table is used for sine and cosine values. When high precision, high speed and a small table are desired, the trigonometric interpolator can be implemented using an angle-rotation processor that is also described here.

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Santa Clara, CA, United States of America

Dengwei Fu