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Round-off Effects in IIR Digital Filters 553
Thus ŷ(n) =± 1 for n ≥ 5. The desired output y(n) is
8
{ 7
y(n) =
8 , − 7
16 , 7 32 , − 7
}
64 , 7
128 , ···, → 0
Hence the error sequence is
e(n) =ŷ(n) − y(n) =
{
0, − 1
16 , 1 32 , − 1
}
64 , 9
128 , ···, →±1 8
(10.27)
(10.28)
This shows that the error e(n) slowly builds up to ± 1 . Hence the error is
8
asymptotically periodic with period 2.
□
From Example 10.5, it is clear that, in the steady state, the system
has poles on the unit circle and hence the nonlinear system has effectively
become a linear system [12]. This implies that, effectively, for the system
in (10.24)
{ ŷ(n − 1), α > 0,
Q [αŷ(n − 1)] =
(10.29)
−ŷ(n − 1), α