Circuit for transforming rectangular coordinates to polar coordinates

Abstract

A circuit for transforming to polar coordinate form first and second binary number electrical signals representative of rectangular coordinates or quadrature components for a vector or phasor. The circuit utilizes a programmable memory in which values corresponding to the sine and cosine functions are stored. In the preferred form, the circuit utilizes binary number electrical signals of 10 bits. The most significant bit of the polar coordinate angle is found directly from the binary number representing one of the quadrature components, whereas the next two most significant bits of the angle are found using logic circuitry in association with the binary number signals representing the quadrature components. The remaining bits of the angle are found by use of a successive approximation technique in conjunction with the values stored in the memory. Once the angle is determined, the amplitude of the vector or phasor is determined by the use of the function P = Im(sin.theta.) + Re(cos.theta.) where Im and Re are the quadrature components. The coordinate transforming circuit is particularly useful in digital transmission and receiving systems in connection with modulation of transmitted signals and demodulation of received signals.