Page 528 - DSP Integrated Circuits

11.17 Complex Multipliers 513

Now, the product of two complex numbers can be written
K X = (CA - DB) + j(DA + CB)
W l
~ - -- ~ w

-w.

_ -
— _•_ ! -W d
l
D(a 0 -a 0 )2 .-a-)2" ~ -D2
i = 1
(11.55)
W.,-1
-w^

,-1
F 1(0,0)2

+ F 2 (0,0)2
i = 1

Hence, the real and imaginary parts of the product can be computed using just
two distributed arithmetic units. The binary functions FI and F% can be stored in a
ROM, addressed by the bits a; and &/. The ROM content is shown in Table 11.5.

«£ bi fl F 2
0 0 -(C-D) -(C + D)
0 1 -(C + D) (C-D)
1 0 (C + D) -{C-D)
1 1 (C-D) (C + D)
Table 11.5 ROM contents for the complex multiplier

It is obvious from Table 11.4 that only two coefficients are needed: (C + D) and
(C - D). The appropriate coefficients can be directed to the accumulators via a 2:2-
multiplexer. If aj © 6j = 1 the values are applied directly to the accumulators, and if
ai © bi = 0 the values are interchanged. Further, the coefficients are either added to,
or subtracted from, the accumulators registers depending on the data bits a; and 6j.
Generally, the number of clock cycles is W^+l, because of the last term in
both the real and imaginary parts in Equation (11.55). However, the number
can be reduced to only Wd, since these values are data independent and they