Optical adaptive linear predictors

Jonathan D. Cohen

doi:10.1364/AO.24.004247

Applied Optics
Vol. 24,
Issue 23,
pp. 4247-4259
(1985)
•https://doi.org/10.1364/AO.24.004247

Optical adaptive linear predictors

Jonathan D. Cohen

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Jonathan D. Cohen, "Optical adaptive linear predictors," Appl. Opt. 24, 4247-4259 (1985)

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Abstract

Adaptive linear predictors have found important application in channel equalization, source redundancy removal, speech encoding and analysis, interference and noise rejection, signal classification, adaptive control, and adaptive antenna systems. In an effort to provide adaptive linear predictors of wide bandwidth, several optical implementations have been proposed. This paper reviews and analyzes the existing optical architectures, putting them in a common framework. Four new common-path architectures are proposed and compared with the others.

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#	Domain	Integration Type	Author	Common Path	Det. Type	Integration Time (sec)	Light-to- light mod	F _r (t,τ)	Comments
1	Time	T/S	Rhodes, Brown	Yes	W	10⁻³	Yes	$p_{0} (τ) e^{- 2 γ τ} e^{- t / τ_{r}}, t > 0$	Needs 50% diffraction eff., Medium bandwidth
2	Time	T/S	Penn, et al.	Yes	P	10⁻³	Yes	$p_{0} (τ) e^{- 2 γ τ} e^{- t / τ_{r}}, t > 0$	Wide bandwidth, Multichannel capability, Uses undiff. light
3	Freq.	S/T/S	Rhodes, Brown		W	10⁻⁵	Yes	$e^{- τ / τ_{r}} p_{0} (τ) e^{- γ t} [1 - e^{- γ (T_{i} - t)}], τ > 0$	Wide bandwidth
4	Freq.	S/T/S	Newman	Yes	W	10⁻⁵	Yes	$e^{- τ / τ_{r}} p_{0} (τ) e^{- γ t} [1 - e^{- γ (T_{i} - t)}], τ > 0$	Wide bandwidth, Uses undiff. light
5	Freq.	S	Vander Lugt		W	10⁻⁵		p₀(τ) p₀(t) p₀(τ + t) e⁻^γ⁽ ^τ ⁺ ^t ⁾
6	Freq.	S	†	Yes	W	10⁻⁵		$p_{0} (τ) p_{0} (t) p_{0} (τ + t) e^{- γ (τ + 2 t)} [1 - e^{- γ (T_{i} - t)}]$	Lose 1/2 bandwidth
7	Freq.	S	†	Yes	W	10⁻⁵		p₀(τ)p₀(t)p₀(τ + t) e⁻^γ⁽ ^τ ⁺ ^t ⁾[1−t/T _i ]	Uses undiff. light
8	Time	S	†	Yes	P	10⁻⁵		p₀(τ) p₀(t) p₀(τ + t)e⁻^γ⁽ ^τ ⁺ ^t ⁾	Lose 1/2 bandwidth
9	Time	S	†	Yes	P	10⁻⁵		p₀(τ)p₀(t)p₀(τ + t)e⁻^γ⁽ ^τ ⁺ ^t ⁾	Uses undiff. light

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Applied Optics