Biomedical Engineering Reference
In-Depth Information
f
l
f
2
BW
FIGURE 3.1
:
Frequency response plot. The 3 dB or 0.707 magnitude point shown in bold
horizontal line determines the low- and high-frequency cutoff points
3.2.2 Time-Bandwidth Product
What is time-bandwidth product? Another concept in characterizing signals is time-
bandwidth product, which is the product (
T
e
W
e
) of the signal time duration and the
signal bandwidth as given in (3.13).
⎡
⎤
dx
(
t
)
dt
2
1
2
−∞
−∞
dt
t
0
)
2
x
2
(
t
)
dt
⎣
⎦
(
t
−
1
2
TW
=
(
T
e
)(
W
e
)
=
∞
−∞
∞
−∞
(3.13)
π
x
2
(
t
)
dt
x
2
(
t
)
dt
1
4
. Small values of
the time-bandwidth product are associated with very simple signals. Large values imply
complex structure and large information content. The time-bandwidth product is a
parameter for judging the usefulness of a given signal in conveying information.
No signal can have a time-bandwidth product smaller than
π
3.2.3 Dimensionality
What is the dimensionality of a signal? Signal dimensionality is a concept closely related
to time-bandwidth product. Dimensionality of a signal is the smallest number of basis
functions needed to achieve a reasonable approximation with a finite number of coeffi-
cients. Signal dimensionality is defined as twice the time-bandwidth product plus one.
The equation for the dimensionality of a signal is given in (3.14).
D
=
2
WT
+
1
(3.14)
where
W
is the bandwidth of the signal, and
T
the time duration of the signal.
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