Design and performance analysis of fiber-optic infinite-impulse response filters

Anjan Ghosh; Steve Frank

doi:10.1364/AO.31.004700

Applied Optics
Vol. 31,
Issue 23,
pp. 4700-4711
(1992)
•https://doi.org/10.1364/AO.31.004700

Design and performance analysis of fiber-optic infinite-impulse response filters

Anjan Ghosh and Steve Frank

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Anjan Ghosh and Steve Frank, "Design and performance analysis of fiber-optic infinite-impulse response filters," Appl. Opt. 31, 4700-4711 (1992)

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Abstract

Design of direct forms of infinite-impulse response digital filters using radiatively tapped fiber-optic delay lines is discussed. Infinite-impulse response filters are attractive because they can provide better magnitude characteristics and sharp transition bands in their frequency response for a smaller number of taps than finite-impulse response filters can. The designs described here use spatial-light modulators and thus can be incorporated into optical adaptive filters for processing light-wave signals. Models of error sources in the fiber-optical realization and their effects on both time- and frequency-response characteristics are explained. Cascading of lower-order subsystems to obtain higher-order filters is discussed. A possible way of reducing the insertion loss using erbium-doped fiber-optic amplifiers is derived.

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FOTDL Type	Direct Form 1	Direct Form 2
Bundles	$\frac{P_{out}}{P_{in}} = \frac{{}^{1}/_{9} f_{1} f_{2} t_{1} (b_{0} + b_{1} + b_{2})}{1 - ⅓ f_{2} t_{1} Γ (a_{1} + a_{2})}$	$\frac{P_{out}}{P_{in}} = \frac{⅕ f_{1} f_{2} t_{1} t_{2} (b_{0} + b_{1} + b_{2})}{1 - ⅕ f_{1} f_{3} t_{1} t_{3} Γ (a_{1} + a_{2})}$
LACE	$\frac{P_{out}}{P_{in}} = \frac{½ f_{1} t_{1} [α_{0} b_{0} + (1 - α_{0}) α_{1} b_{1} + (1 - α_{0}) (1 - α_{1}) α_{2} b_{2}]}{1 - ½ f_{1} f_{2} t_{1} t_{2} Γ [β_{1} a_{1} + (1 - β_{1}) β_{2} a_{2}]}$	$\frac{P_{out}}{P_{in}} = \frac{f_{1} f_{3} t_{1} t_{3} {α_{0} b_{0} + (1 - α_{0}) α_{1} b_{1} + [1 - (α_{1} + β_{1})] (1 - α_{0}) α_{2} b_{2}}}{1 - f_{1} f_{2} r_{1} t_{3} Γ {(1 - α_{0}) β_{1} a_{1} + [1 - (α_{1} + β_{1})] (1 - α_{0}) β_{2} a_{2}}}$

FOTDL Type	Direct Form 1	Direct Form 2
Bundles	$Γ_{b 1} < \frac{3}{f_{2} t_{1} (a_{1} + a_{2})}$	$Γ_{b 2} < \frac{5}{f_{1} f_{3} t_{1} t_{3} (a_{1} + a_{2})}$
LACE	$Γ_{l 1} < \frac{2}{f_{1} f_{2} t_{1} t_{2} [β_{1} a_{1} + (1 - β_{1}) β_{2} a_{2}]}$	$Γ_{l 2} < \frac{1}{f_{1} f_{2} r_{1} t_{3} {(1 - α_{0}) β_{1} a_{1} + [1 - (α_{1} + β_{1})] (1 - α_{0}) β_{2} a_{2}}}$

FOTDL Type	Direct Form 1	Direct Form 2
Bundles	$\frac{P_{out}}{P_{in}} = \frac{{}^{1}/_{9} f_{1} f_{2} t_{1} (b_{0} + b_{1} + b_{2})}{1 - ⅓ f_{2} t_{1} Γ (a_{1} + a_{2})}$	$\frac{P_{out}}{P_{in}} = \frac{⅕ f_{1} f_{2} t_{1} t_{2} (b_{0} + b_{1} + b_{2})}{1 - ⅕ f_{1} f_{3} t_{1} t_{3} Γ (a_{1} + a_{2})}$
LACE	$\frac{P_{out}}{P_{in}} = \frac{½ f_{1} t_{1} [α_{0} b_{0} + (1 - α_{0}) α_{1} b_{1} + (1 - α_{0}) (1 - α_{1}) α_{2} b_{2}]}{1 - ½ f_{1} f_{2} t_{1} t_{2} Γ [β_{1} a_{1} + (1 - β_{1}) β_{2} a_{2}]}$	$\frac{P_{out}}{P_{in}} = \frac{f_{1} f_{3} t_{1} t_{3} {α_{0} b_{0} + (1 - α_{0}) α_{1} b_{1} + [1 - (α_{1} + β_{1})] (1 - α_{0}) α_{2} b_{2}}}{1 - f_{1} f_{2} r_{1} t_{3} Γ {(1 - α_{0}) β_{1} a_{1} + [1 - (α_{1} + β_{1})] (1 - α_{0}) β_{2} a_{2}}}$

FOTDL Type	Direct Form 1	Direct Form 2
Bundles	$Γ_{b 1} < \frac{3}{f_{2} t_{1} (a_{1} + a_{2})}$	$Γ_{b 2} < \frac{5}{f_{1} f_{3} t_{1} t_{3} (a_{1} + a_{2})}$
LACE	$Γ_{l 1} < \frac{2}{f_{1} f_{2} t_{1} t_{2} [β_{1} a_{1} + (1 - β_{1}) β_{2} a_{2}]}$	$Γ_{l 2} < \frac{1}{f_{1} f_{2} r_{1} t_{3} {(1 - α_{0}) β_{1} a_{1} + [1 - (α_{1} + β_{1})] (1 - α_{0}) β_{2} a_{2}}}$

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Equations (13)

Applied Optics