US 6,874,006 B1 · Apparatus and method for rectangular-to-polar conversion

Abstract

A rectangular-to-polar-converter receives a complex input signal (having X0 and Y0 components) and determines an angle φ that represents the position of the complex signal in the complex plane. The rectangular-to polar-converter determines a coarse angle φ1 and a fine angle φ2, where φ=φ1+φ2. The coarse angle φ1 is obtained using a small arctangent table and a reciprocal table. These tables provide just enough precision such that the remaining fine angle φ2 is small enough to approximately equal its tangent value. Therefore the fine angle φ2 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.

Claims24

Dependent claims

In a digital device, a method of generating an output signal that represents a polar angle φ for a complex input signal, the method comprising the steps of:

(1) receiving the complex input signal having a real X0 component and an imaginary Y0 component;
(2) determining an angle φ1 that is a coarse approximation to the angle φ, including the steps of
(2a) determining a Z0 value that approximates a [1/X0] value, wherein [X0] is a truncated approximation of said X0 component,
(2b) digitally multiplying said Z0 value by Y0, resulting in a [Y0 Z0] value, and
(2c) determining an arctan of said [Y0Z0] value, resulting in said angle φ1;
(3) determining a fine adjustment angle φ2, including the steps of
(3a) digitally computing an intermediate complex number, based on said [Y0/X0] value, said intermediate complex number having a real X1 component and an imaginary Y1 component,
(3b) determining a Z1 that approximates a [1/X1] value, wherein [X1] is a truncated approximation of said X1 component,
(3c) digitally multiplying said X1 component by said [Z1] value to produce a Z1X1 component, and digitally multiplying said Y1 component by said [Z1] component to produce a Z1Y1 component,
(3d) determining a one's complement of said Z1X1 component, and
(3e) digitally multiplying said two's complement of said Z1X1 component by said Z1Y1 component, resulting in said fine adjustment angle φ2;
and
(4) adding said fine adjustment angle φ2 to said angle φ1 to form said output signal that is data used by said digital device.

10 more elements

Dependencies are inferred from the claim text.

Apparatus and method for rectangular-to-polar conversion

Life of this patent

Apparatus and method for rectangular-to-polar conversion

Life of this patent

Abstract

Claims24