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CALCULUS OF VARIATIONS
Matched filter receivers
Chernoff bound detection filters
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algorithm amplitude response analysis approximation avalanche gain bandwidth Calculus of Variations chapter characteristic Chernoff bound circuit coefficient-matching coefficients complex component values considered constraint equation convergence curves defined differentiable direct search equaliser error criterion error function error space error surface Euler-Lagrange equation evaluation example exploratory move fibre filter design frequency domain Gauss-Newton generalised given gradient impulse response infinity input integration intersymbol interference iterations Jacobian Lagrange multiplier Lagrangian line search linear log mgf matched filter matrix maximisation minimum noise power obtained optical communication optical receivers optimal optimand optimisation problem optimum output pulse parameters photodiode Poisson process quadratic quasi-Newton method ratio realisation result saddle point sample scalar Section shown in Fig signal simple solution solve specification stationary point conditions strategy target techniques thermal noise transfer function University of Essex variables vector whitened matched filter zero