Digital Signal Processing Reference
In-Depth Information
x
[
n
]
x
[
n
1]
D
Figure 10.12
Representation of a delay.
10.6
BLOCK DIAGRAMS
In Section 9.5, the representation of discrete-time systems by block diagrams was in-
troduced. In this section, we extend these representations to LTI systems described
by difference equations.
The representation of difference equations by block diagrams requires the use
of an ideal delay, as discussed earlier. We use the block shown in Figure 10.12 to
represent this delay. Recall that if the signal into an ideal delay is
x
[
n
], the signal out
at that instant is
We express the operation in Figure 10.12 in the standard form
x[n - 1].
x[n] : y[n] = x[n - 1].
(10.64)
One implementation of an ideal delay uses a memory location in a digital computer.
One digital-computer program segment illustrating this implementation is given by
the two statements
o
XNMINUS1 = X
X = XN
o
This segment applies to many high-level languages. In this segment, X is the memory
location, XNMINUS1 is the number shifted out, and XN is the number shifted in.
Note that the delay is
not
realized if the two statements are reversed in order; if the
number XN is shifted in first, the number X stored in the memory location is over-
written and lost. This delay will now be used in an example.
Simulation diagram for a discrete system
EXAMPLE 10.12
In Section 10.4, we considered a discrete-time system described by the difference equation
y[n] - 0.6y[n - 1] = x[n].
(10.65)
We now find a block diagram, constructed of certain specified elements, that satisfies this
equation. The difference equation can be written as
y[n] = 0.6y[n - 1] + x[n].
