US4747067A
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Apparatus and method for approximating the magnitude of a complex number
Assignee: Raytheon Co
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Filing: 1986-10-14
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Granted: 1988-05-24
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Expires: 2006-10-14
Abstract
Abstract Vector magnitude approximating logic using logarithms of the vector's orthogonal components to select multiplier scaling constants and to minimize arithmetic-function and hardware complexity. The apparatus is particularly applicable to a high-throughput, pipelined, digital signal processing application such as radar. The vector magnitude is approximated by multiplying each component of a complex number representing the vector by selected scaling constants and then by summing the two resulting products. The scaling constants are selected by feeding each orthogonal component of the vector into one of two identical logic arrays which determine the base-2 logarithm of the absolute value of each component. The resulting logarithm values are fed, in parallel, into a third logic array which outputs an address to real and imaginary constant read-only memory generators for providing respective scaling constant pairs which are used to compute the approximate magnitude of the vector or complex number representing the vector.
Inventors
- 👤 Anthony J. Jagodnik, Jr.
- 👤 Ronald C. Evett
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-04 19:15
CPC Classifications
G; G06; G06F; G06F7/00; G06F7/38; G06F7/48; G06F7/4806; G06F7/544; G06F7/552; G06F2207/00; G06F2207/552; G06F2207/5525
Claims Analysis
Total Claims: 44
Claim 1
Independent Claim
138 words
Apparatus for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising: means for generating a logarithm of an absolute value of said real component X and a logarithm of an absolute value of said imaginary component Y of said complex number; means coupled to said logarithm generating means for selecting a scaling constant pair in accordance with an address formed by said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y, said constant pair comprising a real constant K x and an imaginary constant K y ; and means coupled to said constant pair selecting means, to said real component X, and to said imaginary component Y for computing said approximate magnitude of said complex number.
Claim 2
Dependent Claim
138 words
Apparatus for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising: means for generating a logarithm of an absolute value of said real component X and a logarithm of an absolute value of said imaginary component Y of said complex number; means coupled to said logarithm generating means for selecting a scaling constant pair in accordance with an address formed by said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y, said constant pair comprising a real constant K x and an imaginary constant K y ; and means coupled to said constant pair selecting means, to said real component X, and to said imaginary component Y for computing said approximate magnitude of said complex number.
Claim 3
Dependent Claim
14 words
The apparatus recited in claim 1 wherein: said logarithm is computed to the base-2.
Claim 4
Dependent Claim
31 words
The apparatus recited in claim 1 wherein: said real component X and said imaginary component Y of said complex number comprise two's complement binary word inputs to said logarithm generating means.
Claim 5
Dependent Claim
42 words
The apparatus recited in claim 1 wherein: said address for selecting a scaling constant pair is formed by concatenating said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y.
Claim 6
Dependent Claim
24 words
The apparatus recited in claim 1 wherein: said logarithm generating means comprises means for generating logarithms symmetrical about zero for positive and negative inputs.
Claim 7
Dependent Claim
47 words
The apparatus recited in claim 1 wherein: each constant pair for a quadrant of a coordinate system being applicable to all quadrants in accordance with a sign of said real component X and a sign of said imaginary component Y, said coordinate system representing a complex plane.
Claim 8
Dependent Claim
32 words
The apparatus recited in claim 1 wherein: said constant pair is selected to obtain a desired error characteristic over all possible values of said real component X and said imaginary component Y.
Claim 9
Dependent Claim
14 words
The apparatus recited in claim 1 wherein said logarithm generating means comprises logic arrays.
Claim 10
Dependent Claim
15 words
The apparatus recited in claim 1 wherein: said constant pair selecting means comprises logic arrays.
Claim 11
Dependent Claim
173 words
Apparatus for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising: means for generating a logarithm of an absolute value of said real component X and a logarithm of an absolute value of said imaginary component Y of said complex number; means coupled to said logarithm generating means for selecting a scaling constant pair in accordance with an address formed by said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y, said constant pair comprising a real constant K x and an imaginary constant K y ; means coupled to said constant pair selecting means for multiplying said real component X by said real constant K x portion of said constant pair and said imaginary component Y by said imaginary constnat K y portion of said constant pair forming two products; and means coupled to said multiplying means for combining said products resulting from said multiplying means to form said magnitude.
Claim 12
Dependent Claim
173 words
Apparatus for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising: means for generating a logarithm of an absolute value of said real component X and a logarithm of an absolute value of said imaginary component Y of said complex number; means coupled to said logarithm generating means for selecting a scaling constant pair in accordance with an address formed by said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y, said constant pair comprising a real constant K x and an imaginary constant K y ; means coupled to said constant pair selecting means for multiplying said real component X by said real constant K x portion of said constant pair and said imaginary component Y by said imaginary constnat K y portion of said constant pair forming two products; and means coupled to said multiplying means for combining said products resulting from said multiplying means to form said magnitude.
Claim 13
Dependent Claim
14 words
The apparatus recited in claim 10 wherein: said logarithm is computed to the base-2.
Claim 14
Dependent Claim
31 words
The apparatus recited in claim 10 wherein: said real component X and said imaginary component Y of said complex number comprise two's complement binary word inputs to said logarithm generating means.
Claim 15
Dependent Claim
42 words
The apparatus recited in claim 10 wherein: said address for selecting a scaling constant pair is formed by concatenating said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginar component Y.
Claim 16
Dependent Claim
24 words
The apparatus recited in claim 10 wherein: said logarithm generating means comprises means for generating logarithms symmetrical about zero for positive and negative inputs.
Claim 17
Dependent Claim
44 words
The apparatus recited in claim 10 wherein: each constant pair for a quadrant of a coordinate system being applicable to all quadrants in accordance with a sign of said real component X and said imaginary component Y, said coordinate system representing a complex plane.
Claim 18
Dependent Claim
13 words
The apparatus recited in claim 10 wherein: said combining means comprises adder means.
Claim 19
Dependent Claim
14 words
The apparatus recited in claim 10 wherein said logarithm generating means comprises logic arrays.
Claim 20
Dependent Claim
15 words
The apparatus recited in claim 10 wherein: said constant pair selecting means comprises logic arrays.
Claim 21
Dependent Claim
211 words
Apparatus for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising: means for generating a base-2 logarithm of an absolute value of said real component X and a base-2 logarithm of an absolute value of said imaginary component Y of said complex number; means coupled to said logarithm generating means for selecting a code to select a constant pair for each one of a plurality of regions in a quadrant of a coordinate system; memory means coupled to said code selecting means for storing said constant pair for each of said plurality of regions, each constant pair comprising a real constant K x and an imaginary constant K y ; first multiplier means coupled to said real component X and said memory means for multiplying said real component X by said real constant K x ; second multiplier means coupled to said imaginary component Y and said memory means for multiplying said imaginary component Y by said imaginary constant K y ; and means coupled to an output of said first multiplier means and to an output of said second multiplier means for adding together said output from said first and second multiplier means to obtain said magnitude of a complex number.
Claim 22
Dependent Claim
211 words
Apparatus for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising: means for generating a base-2 logarithm of an absolute value of said real component X and a base-2 logarithm of an absolute value of said imaginary component Y of said complex number; means coupled to said logarithm generating means for selecting a code to select a constant pair for each one of a plurality of regions in a quadrant of a coordinate system; memory means coupled to said code selecting means for storing said constant pair for each of said plurality of regions, each constant pair comprising a real constant K x and an imaginary constant K y ; first multiplier means coupled to said real component X and said memory means for multiplying said real component X by said real constant K x ; second multiplier means coupled to said imaginary component Y and said memory means for multiplying said imaginary component Y by said imaginary constant K y ; and means coupled to an output of said first multiplier means and to an output of said second multiplier means for adding together said output from said first and second multiplier means to obtain said magnitude of a complex number.
Claim 23
Dependent Claim
31 words
The apparatus recited in claim 19 wherein: said real component X and said imaginary component Y of said complex number comprises two's complement binary word inputs to said logarithm generating means.
Claim 24
Dependent Claim
33 words
The apparatus recited in claim 19 wherein: values of said real component X logarithm and said imaginary component Y logarithm are concatenated to form an address for coupling to said code selecting means.
Claim 25
Dependent Claim
18 words
The apparatus recited in claim 19 wherein: said plurality of regions comprises seven sets of said constant pairs.
Claim 26
Dependent Claim
60 words
The apparatus recited in claim 22 wherein: said seven sets of said constant pairs are obtained by storing four sets of said constant pairs and interchanging said real constant K x and said imaginary constant K y within a set depending on a location of each of said regions with respect to a 45 degree line in a complex plane.
Claim 27
Dependent Claim
33 words
The apparatus recited in claim 19 wherein: said constant pair is selected to minimize root means square (RMS) error over all possible values of said real component X and said imaginary component Y.
Claim 28
Dependent Claim
60 words
The apparatus recited in claim 19 wherein: said constant pair for each of said plurality of regions stored in said memory means for said quadrant of a coordinate system being applicable to all quadrants in said coordinate system in accordance with a sign of the values of said real component X and said imaginary component Y of said complex number.
Claim 29
Dependent Claim
14 words
The apparatus recited in claim 25 wherein: said coordinate system represents a complex plane.
Claim 30
Dependent Claim
15 words
The apparatus recited in claim 19 wherein said base-2 logarithm generating means comprises logic arrays.
Claim 31
Dependent Claim
14 words
The apparatus recited in claim 19 wherein said code selecting means comprises logic arrays.
Claim 32
Independent Claim
137 words
A method for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising the steps of: generating a logarithm of an absolute value of said real component X and a logarithm of an absolute value of said imaginary component Y of said complex number; selecting a scaling constant pair in accordance with an address formed by said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y, said constant pair having a real constant K x portion and an imaginary constant K y portion; and computing said approximate magnitude of said complex number in accordance with the values of said constant pair K x and K y , said real component X and said imaginary component Y.
Claim 33
Independent Claim
137 words
A method for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising the steps of: generating a logarithm of an absolute value of said real component X and a logarithm of an absolute value of said imaginary component Y of said complex number; selecting a scaling constant pair in accordance with an address formed by said logarithm of said absolute value of said real component X and said logarithm of said absolute value of said imaginary component Y, said constant pair having a real constant K x portion and an imaginary constant K y portion; and computing said approximate magnitude of said complex number in accordance with the values of said constant pair K x and K y , said real component X and said imaginary component Y.
Claim 34
Dependent Claim
20 words
The method recited in claim 29 wherein: said step of generating a logarithm comprises generating said logarithm to the base-2.
Claim 35
Dependent Claim
57 words
The method recited in claim 29 wherein: said step of selecting a scaling constant pair further comprises the step of having stored in a memory means a plurality of constant pairs for a quadrant of a coordinate system, each of said constant pairs being applicable to at least one of a plurality of regions within said quadrant.
Claim 36
Dependent Claim
58 words
The method recited in claim 29 wherein: said step of selecting a scaling constant pair further comprises the step of using said plurality of constant pairs for all quadrants of a coordinate system in accordance with a sign of said real component X and a sign of said imaginary component Y, said coordinate system representing a complex plane.
Claim 37
Dependent Claim
52 words
The method recited in claim 29 wherein: said step of selecting said scaling constant pair includes having sets of a constant pair selected to minimize root means square (RMS) error over all possible values of said real component X and said imaginary component Y in a coordinate system representing a complex plane.
Claim 38
Independent Claim
234 words
A method for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising the steps of: generating a base-2 logarithm of an absolute value of said real component X of said complex number; generating a base-2 logarithm of an absolute value of said imaginary component Y of said complex number; selecting a code in accordance with an address formed from said logarithm of an absolute value of said real component X and said logarithm of an absolute value of said imaginary component Y, said code being used to select one of a plurality of constant pairs for each one of a plurality of regions in a quadrant of a coordinate system; storing said plurality of constant pairs for said plurality of regions in a memory means, said memory means having a first portion for storing real constants K x of said constant pairs and a second portion for storing imaginary constants K y of said constant pairs; multiplying said real component X by said real constant K x from said first portion of said memory means to obtain a real product term; multiplying said imaginary component Y by said imaginary constant K y from said second portion of said memory means to obtain an imaginary product term; and adding said real product term to said imaginary product term to obtain said magnitude of said complex number.
Claim 39
Independent Claim
234 words
A method for approximating a magnitude of a complex number having a real component X and an imaginary component Y comprising the steps of: generating a base-2 logarithm of an absolute value of said real component X of said complex number; generating a base-2 logarithm of an absolute value of said imaginary component Y of said complex number; selecting a code in accordance with an address formed from said logarithm of an absolute value of said real component X and said logarithm of an absolute value of said imaginary component Y, said code being used to select one of a plurality of constant pairs for each one of a plurality of regions in a quadrant of a coordinate system; storing said plurality of constant pairs for said plurality of regions in a memory means, said memory means having a first portion for storing real constants K x of said constant pairs and a second portion for storing imaginary constants K y of said constant pairs; multiplying said real component X by said real constant K x from said first portion of said memory means to obtain a real product term; multiplying said imaginary component Y by said imaginary constant K y from said second portion of said memory means to obtain an imaginary product term; and adding said real product term to said imaginary product term to obtain said magnitude of said complex number.
Claim 40
Dependent Claim
49 words
The method recited in claim 34 wherein: said steps of generating said logarithm of an absolute value of said real component X and said logarithm of an absolute value of said imaginary component Y further comprises generating logarithms symmetrical about zero for positive and negative values of each component.
Claim 41
Dependent Claim
66 words
The method recited in claim 34 wherein: said step of selecting said code for selecting one of a plurality of constant pairs further comprises the step of using said one quadrant of constant pairs for all quadrants of said coordinate system in accordance with a sign of said real component X and a sign of said imaginary component Y, said coordinate system representing a complex plane.
Claim 42
Dependent Claim
50 words
The method recited in claim 34 wherein: said step of selecting said constant pair includes having sets of constant pairs optimized to minimize root mean square (RMS) error over all possible values of said real component X and said imaginary component Y in a coordinate system representing a complex plane.
Claim 43
Dependent Claim
34 words
The method recited in claim 34 wherein: said step of selecting one of a plurality of constant pairs for said plurality of regions comprises the step of providing seven sets of said constant pairs.
Claim 44
Dependent Claim
76 words
The method recited in claim 38 wherein: said step of providing seven sets of said constant pairs further comprises the step of obtaining said seven sets from four sets of constant pairs by interchanging said real constant K x and said imaginary constant K y within a set in accordance with a location of each of said regions with respect to a 45 degree line in said quadrant of said coordinate system representing a complex plane.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1991-05-24 | 1991-11-23 | 1992-05-24 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1995-05-24 | 1995-11-23 | 1996-05-24 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1999-05-24 | 1999-11-23 | 2000-05-24 | $7700.00 | Window Closed / Lapsed |