Patent ID: 6874006

Claim:
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 X 0 component and an imaginary Y 0 component; (2) determining an angle φ 1 that is a coarse approximation to the angle φ, including the steps of (2a) determining a Z 0 value that approximates a [1/X 0 ] value, wherein [X 0 ] is a truncated approximation of said X 0 component, (2b) digitally multiplying said Z 0 value by Y 0 , resulting in a [Y 0 Z 0 ] value, and (2c) determining an arctan of said [Y 0 Z 0 ] value, resulting in said angle φ 1 ; (3) determining a fine adjustment angle φ 2 , including the steps of (3a) digitally computing an intermediate complex number, based on said [Y 0 /X 0 ] value, said intermediate complex number having a real X 1 component and an imaginary Y 1 component, (3b) determining a Z 1 that approximates a [1/X 1 ] value, wherein [X 1 ] is a truncated approximation of said X 1 component, (3c) digitally multiplying said X 1 component by said [Z 1 ] value to produce a Z 1 X 1 component, and digitally multiplying said Y 1 component by said [Z 1 ] component to produce a Z 1 Y 1 component, ( 3 d ) determining a one's complement of said Z 1 X 1 component, and ( 3 e ) digitally multiplying said two's complement of said Z 1 X 1 component by said Z 1 Y 1 component, resulting in said fine adjustment angle φ 2 ; and (4) adding said fine adjustment angle φ 2 to said angle φ 1 to form said output signal that is data used by said digital device.