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(4.16)
where we can approximate the p/4-DPQSK modulation when the modulation information is
. Let us calculate the maximum frequency deviation, fd, in
a symbol time, Ts, for the above phase changes. p/4-DQPSK modulation only allows 4 possible
u(t)
e0,
p
4
,
p
2
,
3p
4
, p, 
p
4
, 
p
2
, 
3p
4 f
s(t)  A(t) # cos[vct  u(t)]
r 2(t) 
1
2
# A2(t) # cos[2wct  2f(t)]
r 2(t) 
1
2
# A2(t) # cos[2wc t  2p # a(t)  2f(t)]
f(t) a(t)
50,16 r(t)  A(t) # cos[vc t  p # a(t)  f(t)]
yr(t)  K # A4(t) # sin [4f(t)  4f ^
(t)]
y(t)  A4(t) # K # sin [4u(t)  4f(t)  4f ^
(t)]
y(t)  z(t) # v(t)
I 2(t)  Q2(t)  A2(t) # cos[2u(t)  2f(t)  2f ^
(t)]
z(t) 
1
2
# A2(t) # sin [2u(t)  2f(t)  2f ^
(t)]
Q(t)  A(t) sin [u(t)  f(t)  f ^
(t)]
I(t)  A(t) cos [u(t)  f(t)  f ^
(t)]
MODULATION DETECTION TECHNIQUES 177
phase changes per symbol time which we will make use of to calculate the four corresponding frequency
changes. The first 2 phase changes are given as
(4.17)
(4.18)
(4.19)
And the second 2 phase changes are given a follows:
(4.20)
(4.21)
(4.22)
The above analysis shows the four allowable phase changes can be interpreted as four allowable
frequency changes: (Hz).


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