US 4,945,505 A · Cordic apparatus and method for approximating the magnitude and phase of a complex number

Abstract

A cartesian to polar coordinate converter using a cordic magnitude circuit for estimating the magnitude and angle of a vector from its known orthogonal components. The vector is described in cartesian coordinates by the complex number I+jQ. The magnitude of the vector and its angle are approximated by an iterative process of successively rotating the vector toward one of the orthogonal axes and the cordic magnitude circuit is implemented in one very large scale integrated (VLSI) complementary metal-oxide semiconductor (CMOS) chip. In systems using a typical cordic magnitude circuit, accuracy increases in direct proportion to the number of rotations. The increase is accompanied by a need for an increased word size which results in a slower operating speed. The improved cordic magnitude circuit achieves higher precision without the need for a larger word size. The Q processing portion of the improved circuit takes advantage of the fact that each value of Q is reduced by one-half with each succeeding rotation after the first rotation, thereby vacating the most significant bit (MSB) position. By doubling the resultant value of Q, the MSB is refilled and the least significant bit (LSB) is vacated making room to accommodate the precision growth of one LSB associated with the next rotation. For small magnitude vectors, the I processing portion of the magnitude circuit left shifts the I and Q components by two bit positions at each rotation to accommodate two additional bits of precision in both the I and Q words.

Claims35

Dependent claims

Apparatus for determining an approximated magnitude of a complex number or vector comprising:

means having a plurality of stages for computing a real (I) component and an imaginary (Q) component for each of a plurality of vector rotations of fixed decreasing predetermined values of angles such that the value of said Q component is reduced by approximately one-half each of said vector rotations after a first rotation, said I and Q components for each of said vector rotations being computed by one of said plurality of stages respectively, the value of said I component at the end of said rotations being said approximated magnitude;
and
each of said vector rotation stages of said computing means comprising shifting means for shifting said Q component on each rotation after said first rotation into a vacated most significant bit (MSB) position of said Q component resulting from said vector rotations in order to accommodate a one bit LSB growth in the next rotation;
and
said shifting means further comprises means for left justifying said I component and correspondingly shifting said Q component into said vacated MSB position of said Q component before each of said rotations after said first rotation is performed, providing the three most significant bits of said I component are zero.

2 more elements

Apparatus for determining an approximation of a magnitude and phase of a complex number or vector comprising:

means for computing the approximated magnitude of a complex number or vector by computing a real (I) component and an imaginary (Q) component for each of a plurality of vector rotations of fixed decreasing predetermined values of angles such that the value of said Q component is reduced by approximately one-half with each of said vector rotations after a first rotation, the value of said I component at the end of said rotations being said approximated magnitude;
said computing means comprises shifting means for shifting said Q component on each rotation after said first rotation into a vacated mos significant bit (MSB) position of said Q component resulting from said vector rotations in order to accommodate a one bit LSB growth in the next rotation;
said shifting further comprises means for left justifying said I component and correspondingly shifting said Q component into said vacated MSB position of said Q component before each of said rotations after said first rotation is performed, providing th three most significant bits of said I component are zero;
and
means coupled to said computing means for determining the phase of the complex number or vector by using a sign bit of an initial I value and an initial Q value of the complex number and a sign of the Q value computed for each rotation.

2 more elements

A method for determining an approximated magnitude of a complex number or vector comprising the steps of:

computing with a plurality of stages a real (I) component and an imaginary (Q) component for each of a plurality of vector rotations of fixed decreasing predetermined values of angles such that the value of said Q component is reduced by approximately one-half with each of said vector rotations after a first rotation, said I and Q components for each of said vector rotations being computed by one of said plurality of stages respectively, th value of said I component at the end of said rotations being said approximated magnitude;
and
shifting in each of said vector rotation stages of said computing means said Q component on each rotation after said first rotation into a vacated most significant bit (MSB) position of said Q component resulting from said predetermined rotation in order to accommodate a one bit LSB growth in the next rotation;
and
left justifying the I component and correspondingly shifting the Q component into said vacated MSB position of said Q component before each of said rotations after said first rotation is performed, providing the three most significant bits of said I component are zero.

2 more elements

A method for determining an approximation of a magnitude and phase of a complex number or vector comprising the steps of:

computing the approximated magnitude of a complex number or vector with means for computing a real (I) component and an imaginary (Q) component for each of a plurality of vector rotations of fixed decreasing predetermined values of angles such that the value of said Q component is reduced by approximately one-half with each of said vector rotations after a first rotation, the value of said I component at the end of said rotations being said approximated magnitude;
and
shifting said Q component with shifting means included in said computing means on each rotation after said first rotation into a vacated mos significant bit (MSB) position of said Q component resulting from said predetermined rotation in order to accommodate a one bit LSB growth in the next rotation;
left justifying the I component and correspondingly shifting the Q component into said vacated MSB position of said Q component before each of said rotations after said first rotation is performed with said shifting means included in said computing means, providing the three most significant bits of said I component are zero;
and
determining the phase of the complex number or vector with means coupled to said shifting means by using a sign bit of an initial I value and an initial Q value of the complex number and a sign of the Q value computed for each rotation.

3 more elements

A cordic magnitude CMOS integrated circuit for determining an approximation of a magnitude and phase of a complex number or vector comprising:

means for buffering a plurality of input signals, said signals comprising real and imaginary data words specifying a vector input;
mans coupled to said input signals buffering means for computing the approximated magnitude of a complex number or vector by computing a real (I) component and an imaginary (Q) component for each of a plurality of vector rotations of fixed decreasing predetermined values of angles such that the value of said Q component is reduced by approximately one-half with each of said vector rotations after a first rotation, the value of said I component at the end of said rotations being said approximated magnitude, said computing means comprising shifting means for shifting said Q component on each rotation after said first rotation into a vacated most significant bit (MSB) position of said Q component resulting from said predetermined rotation in order to accommodate a one bit LSB growth in the next rotation;
and
means coupled to said computing means for determining the phase of said complex number or vector by using a sign bit of an initial I value and an initial Q value of the complex number and a signal of a Q value computed for each rotation;
scan testing means coupled to said magnitude computing means and said phase determining means for testing the logic circuits used for computing said approximated magnitude and phase in accordance with scan test control signals;
and
means coupled to said computing means said phase determining means and said scan testing means for buffering all output signals from said integrated circuit.

4 more elements

Dependencies are inferred from the claim text.

Cordic apparatus and method for approximating the magnitude and phase of a complex number

Life of this patent

Cordic apparatus and method for approximating the magnitude and phase of a complex number

Life of this patent

Abstract

Claims35