Apparatus and method for demodulating a square root of the sum of two squares
AssigneeChun-Shan Institute of Science and Technology
InventorsYow-Ling Gau, Bor-Chin Wang, Ching-Chun Meng
Life of this patent
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Abstract
An apparatus and method for demodulating a square root of the sum of squares of two inputs I and Q in a digital signal processing are provided. The square root {square root over (I2+Q2)} is approximated by an equation aX +bY, wherein coefficients a and b are special binary numbers. Due to the numbers, the square root {square root over (I2+Q2)} can be quickly computed by the operation of shifting and addition. A plurality of possible approximation values for the coefficients a and b are provided, as well as the use of a comparator to select the maximal one among the possible approximation values.
Claims5
An apparatus for demodulating a square root of the sum of squares of two inputs I and Q in a digital signal processing, said apparatus calculating values of an equation âX+{circumflex over (b)}Y to approximate the value of a square root {square root over (I2+Q2)}, said apparatus comprising:
- an absolute value determining circuit for obtaining positive values X and Y respectively from the inputs I and Q;
- a maximal/minimal value determining circuit for determining a maximal value A and a minimal value B respectively corresponding to the outputs X and Y of said absolute value determining circuit;
- a shifter/adder connected to said maximal/minimal value determining circuit for dividing the ratio of A to B into k divisions, values of â and {circumflex over (b)} of every division being represented as a fraction whose denominator being a power of two;
- by shifting a binary number to the left to multiply the binary number by a power of two and shifting a binary number to the right to divide the binary number by a power of two, the values of the first to the k 2 - th
- divisions according to an equation âA+{circumflex over (b)}B being computed, wherein k is a positive value;
- and
- a comparator for generating a maximal value of the k 2
- outputs of said shifter/adder, said maximal value is the approximation value of the square root {square root over (I2+Q2)}.
A method for demodulating a square root of the sum of two squares of two inputs I and Q in a digital signal processing, comprising the following steps:
- (a) using an equation âX+{circumflex over (b)}Y to approximate the value of a square root {square root over (I2+Q2)}, wherein X=|I| and Y=|Q|;
- (b) dividing the ratio of X to Y into k divisions, values of â and {circumflex over (b)} of every division being represented as a fraction whose denominator being a power of two, wherein k is a positive value;
- (c) by shifting a binary number to the left to multiply the binary number by a power of two and shifting a binary number to the tight to divide the binary number by a power of two, the values of the first to the k-th divisions according to said equation âX+{circumflex over (b)}Y are computed;
- and
- (d) generating a maximal value among the values of the k divisions, said maximal value is the approximation value of the square root {square root over (I2+Q2)}.
Dependencies are inferred from the claim text.