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A(co amplitude analog system analytic approximation arbitrary assume assumption autocorrelation autocovariance bandlimited BL function causal Clearly conclude constant convolution theorem Denoting determine discrete system eigenvalue elaborate energy equals estimate Example expansion exponential factor Figure finite follows from Eq Fourier series Fourier transform Fourier-series coefficients frequency function f given H(co Ha(co Hence Hilbert transform impulse response Inserting integral interval inversion formula Laplace transform linear system low-pass filter maximum mean-square error minimum nonnegative Note obtain optimum orthogonal output p(co pair Papoulis periodic function poles power spectrum Prob problem process x(f Proof properties r-BL R(co random variables rational function S(co satisfies sequence signal signal/(f simulator solution spectral stationary process stochastic process sufficiently Suppose system function system with input tends to zero time-limited transform F(co trigonometric polynomial truncated unit circle variance W(co white noise window Y(co yields