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ContinuousTime Systems Defined by
Nonlinear InputOutput Differential Equations
20 other sections not shown
A(kT applied approximation asymptotically stable bandwidth BIBO stability Butterworth filter coefficients complex number components compute the output Consider continuous-time signal convolution denote derivative determine discrete-time signal discretization DTFT equal Euler approximation EXAMPLE expression finite finite-dimensional first-order Fourier series Fourier transform frequency function h(kT impulse response impulse response h(t initial conditions initial energy input x(t input/output difference equation input/output differential equation input/output operator integral interconnection inverse Laplace transform linear time-invariant continuous-time linear time-invariant discrete-time lowpass filter matrix output response resulting output response y(t periodic signal plotted in Figure poles pulse rational function real number realization RLC circuit sampled signal Section shown in Figure signal x(t sinusoidal stability steady-state response step response suppose system given time-invariant continuous-time system time-invariant discrete-time system transfer function H(s transform pair u(kT unit delayers unit-pulse response v(kT values vector voltage x(kT y(kT yikT z-transform zero