Cordic complex multiplier
First Claim
1. A recursive CORDIC rotator, comprising:
- means for receiving digital data words representing each of the real CR part and the imaginary CI part of a first complex number C;
a first portion including means for rotating each one of the first complex number real CR part and imaginary CI part by a first angular increment α
1 of a selected one of +90° and
-90°
to form an associated one of digital data words I and Q;
a recursion portion including means for rotationally modifying each of the I and Q digital data words, received from the first portion, recursively through each selected one of positive and negative incremental angles α
1, for 2≦
i≦
N, where N is a positive integer greater than 2, and each incremental angle α
i not only less than angle α
1 but also greater than a next incremental angle α
i+1 ;
means for receiving a digital data word representing an angular rotation φ
portion of a second complex number B, expressed in amplitude/rotation angle form, and for controlling the signs of the angle α
1 in the first portion and all of the incremental angles α
1 in the recursion portion to successively approximate the second complex number rotation angle φ
; and
means for providing the first and second parts, after rotational modification through all N angles, respectively as a rotated imaginary-part output digital data word AI substantially equal to (BR CI -BI CR), where BR and BI are respective real and imaginary parts of the second complex number B, and a rotated real-part output digital data word AR substantially equal to (BR CR +BI CI).
1 Assignment
0 Petitions
Accused Products
Abstract
A CORDIC (COordinate Rotation DIgital Computer) subsystem for multiplication of two complex digital numbers B and C, where one number is the sum of real and imaginary data portions, expressed in rectangular form (say Cr or CI), and the other number can be expressed in the rectangular form or can be represented by magnitude data, expressed in polar form (say, |B|, φ). An N-stage CORDIC portion of either recursive or pipeline sequential form, but devoid of multipliers, is used to rotate the I and Q terms of the first number through a phase angle φ of the polar-form multiplier number of the equivalent, taken from the rectangular form. The final computed data are the real and imaginary parts of the product.
109 Citations
20 Claims
-
1. A recursive CORDIC rotator, comprising:
-
means for receiving digital data words representing each of the real CR part and the imaginary CI part of a first complex number C; a first portion including means for rotating each one of the first complex number real CR part and imaginary CI part by a first angular increment α
1 of a selected one of +90° and
-90°
to form an associated one of digital data words I and Q;a recursion portion including means for rotationally modifying each of the I and Q digital data words, received from the first portion, recursively through each selected one of positive and negative incremental angles α
1, for 2≦
i≦
N, where N is a positive integer greater than 2, and each incremental angle α
i not only less than angle α
1 but also greater than a next incremental angle α
i+1 ;means for receiving a digital data word representing an angular rotation φ
portion of a second complex number B, expressed in amplitude/rotation angle form, and for controlling the signs of the angle α
1 in the first portion and all of the incremental angles α
1 in the recursion portion to successively approximate the second complex number rotation angle φ
; andmeans for providing the first and second parts, after rotational modification through all N angles, respectively as a rotated imaginary-part output digital data word AI substantially equal to (BR CI -BI CR), where BR and BI are respective real and imaginary parts of the second complex number B, and a rotated real-part output digital data word AR substantially equal to (BR CR +BI CI). - View Dependent Claims (2, 3, 4, 5)
-
-
6. A sequential CORDIC rotator, comprising:
-
means for receiving digital data words representing each of the real I and imaginary Q parts of a first complex number; a first portion including stage means for separately rotating each one of the first and second complex number real and imaginary parts by a first angular increment α
1 of a selected one of +90° and
-90°
;a second portion including a plurality (N-1) of stage means, where N is a positive integer greater than 2, each for rotationally modifying a pair of input real and imaginary part digital data words through one selected one of a positive and negative incremental angles α
i, for 2≦
i≦
N, with each i-th stage means incremental angle α
i not only less than angle α
1 but also greater than a next stage incremental angle α
i+1, and with the pair of input digital data words to the second portion first stage means being received from the first portion and the pair of input digital data words for any other stage means of the second portion being received from an immediately-previous second portion stage means;means for receiving a digital data word representing an angular rotation φ
portion of a second complex number expressed in amplitude/rotation-angle form, and controlling the signs of the angle α
1 in the first portion and all of the incremental angles α
1 in the plurality of stage means to approximate the second complex number rotation angle φ
; andmeans for providing the first and second parts, after rotational modification through all N angles, respectively as a rotated imaginary-part output digital data word and a rotated real-part output digital data word. - View Dependent Claims (7, 8, 9, 10)
-
-
11. Apparatus for providing output digital data which is the produce of a first complex number C, represented as a real-part digital data word CR and an imaginary-part digital data word CI, and a second complex number B, represented as a magnitude |B| digital data word and a phase angle φ
- digital data word comprising;
input means, receiving at least the first complex number real-part digital data word CR and the imaginary-part digital data word CI, for providing an input real-part digital data word I and an input imaginary-part digital data word O; CORDIC means for rotationally modifying respectively the input real-part digital data word I and the input imaginary part digital data word Q responsive to the phase angle φ
digital data word to respectively obtain an output digital data word Q'"'"' and an output digital data word I'"'"'; andoutput means receiving the respective output Q'"'"' and I'"'"' digital data words for respectively providing an imaginary part AI and a real-part AR of a digital data word for an output complex number A proportional to the product of B and C. - View Dependent Claims (12, 13, 14, 15)
- digital data word comprising;
-
16. Apparatus for providing output digital data which is the product of a first complex number, represented as a real-part digital data word I1, and an imaginary-part digital data word Q1, and a second complex number, represented as a real-part digital data word I2 and an imaginary-part digital data word Q2, comprising:
-
first and second CORDIC means for rotationally modifying by an angle α
i , where i is a positive integer, where α
1 is a selected one of ±
90° and
α
i, for 2≦
i≦
N and N greater than 2, is tan-1 (2-n) with n=i-2, respectively an input real-part digital data word I and an input imaginary-part digital data word Q, responsive in each i-th one of N time intervals to the state of another digital data bit, to respectively obtain an output digital data word Q'"'"' and an output digital data word I'"'"';
the first CORDIC means receiving respective data words I1 and Q1 as respective real-part and imaginary-part data words and providing at least one output data word I0 and a signal which changes sign state when the effective output angle is substantially zero;
the second CORDIC means receiving respective data words I2 and Q2 as respective real-part and imaginary-part data words and providing respective real-part and imaginary-part output data words I" and Q";means for providing in each i-th time interval said another digital data bit with a data state selected to cause both of said CORDIC means to rotationally modify the output digital data words therein until the sign-stage signal changes sign; and output means receiving the respective output I" and Q" digital data words for respectively providing an imaginary-part I'"'"' of the output digital data and a real-part Q'"'"' of the output digital data word. - View Dependent Claims (17, 18)
-
-
19. Apparatus for providing output digital data which is the product of a first complex number, represented as a real-part digital data word I1 and an imaginary-part digital data word Q1, and a second complex number, represented as a real-part digital data word I2 and an imaginary-part digital data word Q2, comprising:
- first and second CORDIC means for rotationally modifying by an angle α
i, where i is a positive integer, where α
1 is a selected one of ±
90° and
α
i, for 2≦
i≦
N and N greater than 2, is tan-1 (2-n) with n=i-2, respectively an input real-part digital data word I and an input imaginary-part digital data word Q, with the sign of each angle responsive to the logic state of an associated sign bit;
the sign bit for each angle of the first means being the data bit then present at one of the pair of data inputs for a computing stage for that angle, to respectively obtain an output digital data word Q'"'"' and an output digital data word I'"'"';a plurality N of means for inverting the logic state of an input bit, each i-th inverting means receiving the sign bit from the stage for the first means for the associated i-th angle and providing another sign bit to the like-numbered i-th stage of the second means; the second means receiving the respective data words I2 and Q2 as respective real-part and imaginary-part data words and providing at least one output word which is the magnitude |A2 | of the second complex number; and output means receiving the respective output I'"'"' and Q'"'"' digital data words for respectively providing an imaginary-part Q" of the output digital data and a real-part I" of the output digital data word. - View Dependent Claims (20)
- first and second CORDIC means for rotationally modifying by an angle α
Specification