Biomedical Engineering Reference
In-Depth Information
TABLE 12.10 SUMMARY OF SYMMETRY TABLES
TABLE A:
Waveform Symmetry
SYMMETRY
CONDITION
ILLUSTRATION
PROPERTY
f
Even
f
(
t
)
=
f
(
−
t
)
cosine terms only
t
T
T
2
-
2
f
Odd
f
(
t
)
=−
f
(
−
t
)
sine terms only
T
t
T
2
-
2
f
Half-wave
f
(
t
)
=−
f
(
t
±
T
/
2)
odd
n
only
t
T
T
2
-
2
TABLE B:
Fourier Transform of Symmetrical Waveforms
PROPERTY
a
0
a
n
(
n
= 0)
b
n
T
/
2
4
T
cosine terms only
*
f
(
t
) cos
n
ω
0
tdt
0
0
T
/
2
4
T
sine terms only
0
0
f
(
t
) sin
n
ω
0
tdt
0
T
/
2
T
/
2
4
T
4
T
Odd
n
only
0
f
(
t
) cos
n
ω
0
tdt
f
(
t
) sin
n
ω
0
tdt
0
0
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