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CALCULUS OF VARIATIONS
Matched filter receivers
Chernoff bound detection filters
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algorithm analysis applied approximation avalanche gain bandwidth Calculus of Variations chapter Chernoff bound circuit coefficient-matching coefficients complex component values considered constraint equation convergence curves defined derivative differentiable direct search equaliser error criterion error function error space error surface Euler-Lagrange equation evaluation example exploratory move f(xu x2 fibre filter design frequency domain function minimisation Gauss-Newton Gauss-Newton method given gradient impulse response infinity input integration intersymbol interference iterations Jacobian Lagrange multiplier Lagrangian line search linear log mgf matched filter matrix maximisation method minimum noise power obtained optical communication optical receivers optimal optimisation problem optimum output pulse parameters photodiode Poisson process pulse shaping quadratic quasi-Newton quasi-Newton method realisation sampling scalar Section shown in Fig signal solution solve specification spectrum stationary point conditions strategy target techniques thermal noise transfer function University of Essex variables vector zero