Graphics Programs Reference
In-Depth Information
h(t)
+
Σ
x(t)
y(t)
-
delay,
T
Figure 7.4. Single delay line canceler.
where
δ⋅
(
)
is the delta function. It follows that the Fourier transform (FT)
of
h
()
is
j
ω
T
H
() 1
=
e
(7.6)
where
ω
=
2π
f
.
In the z-domain, the single delay line canceler response is
1
H
() 1
=
z
(7.7)
The power gain for the single delay line canceler is given by
H
()
2
j
ω
T
e
j
ω
T
H
()
H
∗
() 1
=
=
(
e
) 1
(
)
(7.8)
It follows that
H
()
2
11
e
j
ω
T
j
ω
T
=
+
(
+
e
)
=
21
(
cos
ω
T
)
(7.9)
)
2
and using the trigonometric identity
(
22 2ϑ
cos
)
=
4
(
sin
ϑ
yields
H
()
2
)
2
=
4
(
sin
(
ω
T
⁄
2
)
(7.10)
MATLAB Function Ðsingle_canceler.mÑ
The function
Ðsingle_canceler.mÑ
computes and plots (as a function of )
the amplitude response for a single delay line canceler. It is given in Listing 7.1
in Section 7.11. The syntax is as follows:
f
⁄
f
r
[resp] = single_canceler (fofr)
where
fofr
is the number of periods desired. Typical output of the function
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