Digital Signal Processing Reference
In-Depth Information
e4
a
b
2
1
31
2 3
aa1
aa2
aa3
pp1
pp2
pp3
e1
e3
6
2
e2
c
...
R
a2,1
R
a2,2
...
R
a2,1
R
a2,2
i1
aa1
aa2
aa3
,[0])
,[0])
R
a2,3
R
a2,3
)
)
i2
R
a3,1
...
R
a3,1
...
Fig. 3
Example of concurrent MoCs. (
a
)KPN,(
b
)SDF,(
c
) DDF
require at least 1, 2 and
m
tokens respectively with arbitrary values to be available
at the input. The symbol
⊥
represents any input sequence, including an empty
FIFO. For an actor
a
to be in the ready state at least one of its firing rules need to
actor
a
2
has three different firing rules. This actor is ready if there are at least two
tokens in input
i1
and at least 1 token in input
i2
, or if the next token on input
i2
or
i1
has value 0. Notice that more than one firing rule can be activated, in
this case the dataflow graph is said to be non-determinate.
in which an actor with
p
inputs has only one firing rule of the form
=(
,...,
)
∈
N
R
a
,
1
. Additionally, the amount of tokens produced by
one execution of an actor on every output is also fixed. An SDF can be defined as
agraph
G
n
1
n
p
with
n
3
=(
,
,
)
=
{
,...,
w
|
E
|
}⊂
N
V
E
W
where
W
w
1
associates three integer
=(
,
,
)
=(
,
)
∈
constants
w
e
E
.
p
e
represents the
number of tokens produced by every execution of actor
a
1
,
c
e
represents the
number of tokens consumed in every execution of actor
a
2
and
d
e
represents the
number of tokens (called delays) initially present on edge
e
. An example of an
SDF in the example,
W
p
e
c
e
d
e
to every channel
e
a
1
a
2
=
{
(
,
,
)
,
(
,
,
)
,
(
,
,
)
,
(
,
,
)
}
3
1
0
6
2
0
2
3
0
1
2
2
.
Different dataflow models differ in their expressiveness, some being more
general, some being more restrictive. By restricting the expressiveness, models
possess stronger formal properties (e.g. determinism) which make them more
amenable to analysis. For example, the questions of
termination
and
boundedness
,
i.e. whether an application runs forever with bounded memory consumption, are
