(2.54)
where the roll-off factor, JR the jump rate, and fn Nyquist frequency.
(2.55) H2( f ) ?µ 1 , 0 f (1 a) fn
1
2
Ts
2a
(1 C)af
1
2Tsb , (1 a) fn f (1 a) fn
0 , (1 a) fn f
H1( f ) ?µ 1 , 0 f (1 a) fn
(1 JR)
(1 2 JR)( f afn fn)
2a fn
, (1 a) fn f (1 a) fn
0 , (1 a) fn f
MODULATION THEORY 97
I-Channel
Q-Channel
A
FIGURE 2.80 Cross-correlated baseband waveforms.
Figure 2.81 compares the frequency responses of the RC to that of the DJ filters defined above
[57, 58].
Since these filters satisfy the Nyquist criteria of zero ISI, one can imagine applying the same reasoning
used for the SRC to the square root DJ filter. A comparison of the square root DJ filters (SDJ)
is shown in Fig. 2.82.
98 CHAPTER TWO
Double-Jump Frequency Responses
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized Frequency (Hz)
H( f )
RC, a = 0.5
H1, a = 0.5, JR = 0.1
H2, a = 0.5, C = 0.1
FIGURE 2.81 Double-jump filter frequency response comparison.
Square Root Double-Jump Filter Responses
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized Frequency (Hz)
H( f )
RC, a = 0.
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