Lossless Digital Filter Overflow Oscillations; Approximation of Invariant Fractals
1997 ◽
Vol 07
(11)
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pp. 2603-2610
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Keyword(s):
We investigate second order lossless digital filters with two's complement overflow. We numerically approximate the fractal set D of points that iterate arbitrarily close to the discontinuity. For the case of eigenvalues of the associated linear map of the form eiθ with θ/π ∉ Q we present evidence that D has positive two dimensional Lebesgue measure. For θ/π ∈ Q we confirm that D has Lebesgue measure zero. As a by-product we get estimates of the exterior dimension of D. These results imply that if such filters are realized using finite-precision arithmetic then they will have a sizeable fraction of orbits that are periodic with high period overflows.
1985 ◽
Vol 58
(1)
◽
pp. 159-174
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Keyword(s):
1943 ◽
Vol 39
(1)
◽
pp. 51-53
Keyword(s):
1972 ◽
Vol 19
(4)
◽
pp. 410-413
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2000 ◽
Vol 20
(5)
◽
pp. 1271-1285
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1992 ◽
Vol 40
(9)
◽
pp. 2311-2317
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Keyword(s):
2015 ◽
Vol 93
(2)
◽
pp. 272-282
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