Optimal free parameters in orthonormal approximations

We consider orthonormal expansions where the basis functions are governed by some free parameters. If the basis functions adhere to a certain differential or difference equation, then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error. This expression is a function of the free parameters and some simple signal measurements. Restrictions on the differential or difference equation that make this possible are given. Minimization of either the upper bound or the enforced convergence criterion as a function of the free parameters yields the same optimal parameters, which are of a simple form. This method is applied to several continuous-time and discrete-time orthonormal expansions that are all related to classical orthogonal polynomial

Changes with background in the linear model of the transient visual system

There is evidence that the transient channel of temporal human vision behaves as a linear filter for small excursions around a steady background level. The linear filter characteristics depend on the background level. From experimentally obtained impulse responses of the transient channel the linear filter can be modelled and parametrized. This has been done for two different background levels. The two sets of estimated parameters at these two levels show a shift in the parameters which can be described by a single multiplication factor. This result was extrapolated to arbitrary background levels by postulating that each change in background level can be described by a multiplication factor. This leads to an assumption on the variation of the parameters of the linear filter of the transient channel with changes in the background level. This assumption is tested by simulating the system for different parameter sets of the linear filter. The simulations give a good agreement with experimental data on threshold-versus-duration curves and de Lange curves. The (minor) quantitative differences in simulations and experimental data can be explained