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analog analyst applied approximation assumed bandwidth channel capacity coefficients combination complete condition convex convex function corresponding covariance function criterion decision defined definition detection diagram differential elements entropy equations equivalent error estimate evaluate example expression filter finite formulated Fourier series Fourier transform frequency graph Hilbert transform illustrate implies input signal integral inverse linear system loss function lottery mathematical matrix maximum measure method noise nonlinear normal normally distributed observation obtained operation optimal optimum ordering orthogonal orthogonal polynomials output signal performance parameters perturbation polynomial power spectral density pre-envelope preference probability density function problem pseudoinverse random process random variables relation representation result risk function sample selected signal x(t simulation solution space spectral density function subsystem Suppose symbols system analysis system parameters system performance system specifications technique theorem theory tion vector yield zero