where PS, PJ denote the signal power and interfering tone power, respectively, whereas
jH(!S)j and jH(!J )j denote the corresponding transfer function magnitudes at the signal
and interferer frequencies. Figure 3.2(a) shows a surface plot of SIR improvement as a
function of proximity (closeness of !J to !S) and accuracy (closeness of !0 to !J ) for a
fixed Q (Q=50), while Fig. 3.2(b) displays its contours taken as cross-sections in the xy plane.
The plot indicates that SIR improvement is positively affected as separation between the signal (!S) and interferer frequency (!J ) increases, however, improvement tapers off as
the accuracy of setting the center frequency of the filter degrades. Targeting 40dB SIR
improvement, Figure 3.3 shows fixed (40dB) improvement contours for four filter quality
factor values (Q = 10, 30, 50 and 100). Higher Q filters perform better whenever the center
frequency is accurately set and the interferer is close to the signal; however, a lower Q ofers
better improvement when accuracy is limited and the interferer frequency is much different
from that of the signal. The plot accentuates the need for accurately tracking the interferer
frequency, or !0
= !J .