yn Txn,
3:1:9
where T denotes the computational process for transforming the input signal, x(n), into
the output signal, y(n). A block diagram of the DSP system defined in (3.1.9) is
illustrated in Figure 3.1.
The processing of digital signals can be described in terms of combinations of certain
fundamental operations on signals. These operations include addition (or subtraction),
multiplication, and time shift (or delay). A DSP system consists of the interconnection
of three basic elements ± adders, multipliers, and delay units.
Two signals, x
1
n and x
2
n, can be added as illustrated in Figure 3.2, where
yn x
1
n x
2
n
3:1:10
is the adder output. With more than two inputs, the adder could be drawn as a multi-
input adder, but the additions are typically done two inputs at a time in digital hard-
ware. The addition operation of Equation (3.1.10) can be implemented as the following
C55x code using direct addressing mode:
mov @x1n, AC0 ; AC0 x1(n)
add @x2n, AC0 ; AC0 x1(n)x2(n) y(n)
A given signal can be multiplied by a constant, a, as illustrated in Figure 3.3, where
x(n) is the multiplier input, a represents the multiplier coefficient, and
yn axn
3:1:11
x(n)
DSP system
T [ ]
y(n) = T [x(n)]
Figure 3.1 Block diagram of a DSP system
x
1
(n)
x
1
(n)
x
2
(n)
y(n)
x
2
(n)
y(n)
+
+
or
Figure 3.2 Block diagram of an adder
x(n)
y(n)
a
or
x(n)
y(n)
a
Figure 3.3 Block diagram of a multiplier
80
DSP FUNDAMENTALS AND IMPLEMENTATION CONSIDERATIONS