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Fundamental Concepts and Definitions
Time Invariance Linearity and Basis Functions
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abstract object amplitude associated basis functions becomes coefficients components consider constant continuous-time system correlation function corresponding defined denoted determined differential equation differential operator system differential systems discrete-time discrete-time system eigenvalues eigenvectors elements energy equivalent system ergodic set expression Figure finite follows fundamental matrix gives impulse response input segment space input-output pair input-output relation input-output-state relation integral interval linear system Markov system matched filter mean square error method noise optimum filter partial fractions perturbation polynomial power spectral density probability amplitude process u(t random process readily represented respectively sample function sampled signal satisfies 1.6 scalar product second self-consistency condition separation property signal signal-to-noise ratio solution specific stable stationary Substituting system characterized system of Fig system representation terminal variables Theorem theory tion transfer function transition probability unforced system unit impulse unperturbed vector x(r written x(ro zero input response zero state response zero-state