ETTC'2003 - SEE

2.5 FM demodulation
Fig.9 I ‘(nT1), Q’ (nT1) and their complex spectrum
FM demodulation can be implemented by tan -1 operation. The phase of I’(n) and Q’(n) can be
computed as Eq. 14,
is,
−1
⎡Q'
( n)
⎤
φ '(
n)
= tan ⎢ ⎥ (14)
⎣ I'
( n)
⎦
The instantaneous frequency f ‘(n) can be obtained by differentially detection of φ’(n), that
tan
φ'
( nT ) −φ
'[(
n −1)
T1
]
f '(
n)
=
=
2π
⋅ k ⋅T
f
1
−1
⎡Q'
( n)
⎤ −1
⎡Q'
( n −1)
⎤
⎢ ⎥ − tan ⎢ ⎥
⎣ I'
( n)
⎦ ⎣ I'
( n −1)
⎦
2π
⋅ k ⋅T
A high effective algorithm of CODRDIC (coordinate rotation digital computer) can be used
to perform computation of Eq.14 and 15, which convert between polar and Cartesian coordinates
using shift, add, and subtract operations only. f’(n) and its spectrum are illustrated in fig.10
2.6 PCM demodulation
Fig.10 f’(n) and its sprectrum
Two main functions are included in the PCM demodulation part, the first is to extract timing
error from the FM demodulated data f’(n) and establish bit synchronization, the other is to
interpolate f’(n) to obtain the sample values at strobe points to make decisions for the original
6
f
1
(15)