Connexions module: m26740 1
Carrier Frequency Modulation
∗
Tuan Do-Hong
This work is produced by The Connexions Project and licensed under the
Creative Commons Attribution License
†
1 Frequency Shift Keying (FSK)
The data is impressed upon the carrier frequency. Therefore, the
M
dierent signals are
sm(t) = APT(t) cos (2πfct+ 2π(m−1) ∆ (f)t+θm)
(1)
for
m∈ {1,2, . . . , M }
The
M
dierent signals have
M
dierent carrier frequencies with possibly dierent phase angles since
the generators of these carrier signals may be dierent. The carriers are
f1=fc
(2)
f2=fc+ ∆ (f)
fM=fc−M∆ (f)
Thus, the
M
signals may be designed to be orthogonal to each other.
< sm, sn>=RT
0A2cos (2πfct+ 2π(m−1) ∆ (f)t+θm) cos (2πfct+ 2π(n−1) ∆ (f)t+θn)dt =
A2
2RT
0cos (4πfct+ 2π(n+m−2) ∆ (f)t+θm+θn)dt +
A2
2RT
0cos (2π(m−n) ∆ (f)t+θm−θn)dt =A2
2
sin(4πfcT+2π(n+m−2)∆(f)T+θm+θn)−sin(θm+θn)
4πfc+2π(n+m−2)∆(f)+
A2
2sin(2π(m−n)∆(f)T+θm
−θn)
2π(m−n)∆(f)−sin(θm
−θn)
2π(m−n)∆(f)
(3)
If
2fcT+(n+m−2) ∆ (f)T
is an integer, and if
(m−n) ∆ (f)T
is also an integer, then
< Sm, Sn>= 0
if
∆ (f)T
is an integer, then
< sm, sn>'0
when
fc
is much larger than
1
T
.
In case
∀m, θm= 0 : (θm= 0)
< sm, sn>'A2T
2sinc (2 (m−n) ∆ (f)T)
(4)
Therefore, the frequency spacing could be as small as
∆ (f) = 1
2T
since
sinc (x)=0
if
x=±(1)
or
±(2)
.
∗
Version 1.1: Jul 3, 2009 8:09 am GMT-5
†
http://creativecommons.org/licenses/by/3.0/
http://cnx.org/content/m26740/1.1/
