of Microprocessors

DIGITAL TONE GENERATION TECHNIQUES
447
10
15 I
1 0 II /5
1
ooסס 1000
X X
0'100 1100 0010 1010 0110 1110 -0001 1001 0101 1101 0011 1011 0111 1111
0000 0001 0010 0011 0100 0101 OHO 0111 1000 1001 1010 10~1 1100 1101 1110 '1'1
Fig. 13-12. Stages in decimation of a 16-sample record
consider the complex number as a compact method of representing a pair of
closely related but independent numbers. Accordingly, complex numbers
will be represented here as two ordinary numbers, real part first, separated by
a comma in a manner much like the two-dimensional coordinates of a point.
The cosine and sine multipliers used in the computation are also considered
to be complex numbers. Previously we used the cosine and sine of an
angle that incremented by 27T/N for the fundamental, 47T/N for the second
harmonic, etc. Now the cosine and sine ofthe angle will be treated as a single
complex number. Since the angles are always an integer times 27T/N, we can
define a complex function, W, such that W(I) =cos(27TI/N) ,sin(27TI/N),
where I is any integer and N is the number of points in the record under