Digital Signal Processing Reference
In-Depth Information
In conclusion
DTFT
−
1
1
+
1
/
2 r
n
≥
0
= ˆ
u
[
n
]=
l
g
r
,
y
i
d
.
,
©
,
L
s
e
−j
ω
1
−
/
<
−
1
2 r
n
0
But this is almost good! Indeed,
1
2
u
[
n
]=ˆ
u
[
n
]+
so that finally the DTFT of the unit step is
1
1
2
˜
e
j
ω
)=
U
(
e
−j
ω
+
δ
(
ω
)
(4.91)
1
−
and its magnitude is sketched in Figure 4.28.
-
π
-
π/
2
0
π/
2
π
Figure 4.28
Magnitude spectrum for the unit step.
Further Reading
A nice engineering topic on Fourier theory is
The Fourier Transform and Its
Applications
, by R. Bracewell (McGraw- Hill, 1999). A more mathematically
oriented textbook is
Fourier Analysis
,byT.W.Korner(CambridgeUniver-
sity Press, 1989), as is P. Bremaud's book,
Mathematical Principles of Signal
Processing
(Springer, 2002).
