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# Fast and Accurate Computation of the Amplitude of Quadrature Pairs

IP.com Disclosure Number: IPCOM000121623D
Original Publication Date: 1991-Sep-01
Included in the Prior Art Database: 2005-Apr-03
Document File: 2 page(s) / 58K

IBM

## Related People

Raghavan, SA: AUTHOR

## Abstract

Accurate determination of the amplitude of a quadrature pair is a necessity in many signal processing applications. It is also useful in digital PES demodulation of the servo system for a partial response maximum likelihood (PRML) system. The exact determination of a quadrature pair involves doubling the number of bits and also finding the square root, which is a sequential process and, hence, time-consuming. The new method described in this article is very attractive from the standpoint of accuracy and speed. This method is called "2-Step Least Square Estimate" (2-LSE). This estimate is obtained by using piecewise linear approximation of a function. The number of steps in the estimate refer to the number of linear functions used to approximate the given function.

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Fast and Accurate Computation of the Amplitude of Quadrature Pairs

Accurate determination of the amplitude of a quadrature
pair is a necessity in many signal processing applications.  It is
also useful in digital PES demodulation of the servo system for a
partial response maximum likelihood (PRML) system.  The exact
determination of a quadrature pair involves doubling the number of
bits and also finding the square root, which is a sequential process
is very attractive from the standpoint of accuracy and speed. This
method is called "2-Step Least Square Estimate" (2-LSE).  This
estimate is obtained by using piecewise linear approximation of a
function.  The number of steps in the estimate refer to the number of
linear functions used to approximate the given function.  For a given
number of steps, the best linear approximation is obtained by
minimizing the total mean squared error of the estimate and, hence,
the name LSE.  This estimate has a worst- case error of only 1.32%

The 2-LSE for the amplitude of quadrature pairs is shown
graphically in Fig. 1.  If we call the quadrature pair X and Y, and
their amplitude A, then A is given by

Let us assume that X and Y are non-negative (if they are
negative, their absolute values can be taken).  If we call A' the
2-LSE of A, then A' can be written in the form
A' = C1X+C2Y
in either of the two pieces of the linear a...