Digital Signal Processing Reference
In-Depth Information
State
Input Buffer0
Write Port
f
a
Output Buffer0
Read Ports
f
b
Input Buffer1
Controller
Enable Signal
Fig. 21
A simple SBF actor
function state
. A selected function is
enabled
when all its input arguments can be
read, and all its results can be written; it is blocked otherwise. A selected non-
blocked function must evaluate or
fire
. Arguments and results are called
input tokens
and
output tokens
, respectively.
An actor operates on sequences of tokens, streams or signals, as a result of a
repetitive enabling and firing of functions from the function repertoire. Tokens are
read
from external ports and/or loaded from private memory, and are
written
to
external ports and/or stored in private memory. The external ports connect to FIFO
channels through which actors communicate point-to-point.
Figure
21
depicts an illustrative stream-based function (SBF) actor. Its function
repertoire is
P
=
{
,
,
f
b
}
. The two read ports, and the single write port connect
to two input and one output FIFO channels, respectively.
P
contains at least an
initialization function
f
init
, and is a finite set of functions. The functions in
P
must be
selected in a mutual exclusive order. That order depends on the controller's selection
and transition function. The private memory consists of a function state part, and a
data state part that do not intersect.
f
init
f
a
8.2
The Formal Model
If
C
denotes the SBF actor's function state space, and if
D
denotes its data state
space, then the actor's state space
S
is the Cartesian product of
C
and
D
,
S
=
C
×
D
,
C
∩
D
=
0
.
(2)
C
be the current function state. From
c
, the controller selects a function
and makes a function state transition by activating its selection function
Let
c
∈
μ
and
transition function
ω
as follows,
μ
:
C
→
P
,
μ
(
c
)=
f
,
(3)
c
.
ω
:
C
×
D
→
C
,
ω
(
c
,
d
)=
(4)
