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Feedback Control in Systems Biology
book

Feedback Control in Systems Biology

by Carlo Cosentino, Declan Bates
October 2011
Intermediate to advanced content levelIntermediate to advanced
296 pages
9h 39m
English
CRC Press
Content preview from Feedback Control in Systems Biology
Linear systems 27
A fundamental res ult in Fourier analysis is that any periodic function f(t)
with period T can be wr itten as
f(t) = F
0
+
X
n=1
[F
cn
cos(
0
t) + F
sn
sin(
0
t)] ,
where ω
0
= 2π/T , and
F
0
=
1
T
Z
T
f(t)dt ,
F
cn
=
2
T
Z
T
f(t) cos(
0
t)dt , F
sn
=
2
T
Z
T
f(t) sin(
0
t) .
Note that F
0
is the average value of f (t) over a single period.
Example 2.3
Consider the square wave signal
P
w
(t) =
1 if 0 < t T/2
0 if T/2 < t T
Using the formula above we can easily compute the Fourier coefficients
F
0
=
1
2
, F
cn
= 0 n N , F
sn
=
2
if n is odd
0 if n is even
.
Therefore, the square wave can be written
P
w
(t) =
1
2
+
2
π
sin(ω
0
t) +
2
3π
sin(3ω
0
t) +
2
5π
sin(5ω
0
t) + ··· (2.13)
Fig. 2.4 shows different ...
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Publisher Resources

ISBN: 9781439816912