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algorithm amplitude analog-computer diagram analysis approximation behavior calculation causal system Chap characteristic equation characteristic function circuit coefficients components Consider constant continuous-time systems contour converges correlation function corresponding cosh defined definition denote derivative determine difference equation differential equations discrete-time system discrete-time transfer function eigenvalues evaluated Example exponentials expression filter finite Fourier series Fourier transform frequency fundamental matrix given Hence Hurwitz polynomial imaginary axis impulse response initial conditions input x(t instant integral interval inverse Laplace transform linear system method normal form obtain poles power spectral density Prob problem pulse random process random variables relation result right half plane roots sample functions shown in Fig sinh solution spectrum stability stationary stationary process system is stable theorem Theory time-invariant time-varying system tion transfer function transmission line unit circle unit impulse unit step vector voltage white noise zero